1. The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member?
Solution:
Let the members be Old Having age O + other 9 having ages x and New one having age Y
Sum of their ages = (Y + 9 × x) and average = (Y + 9 × x)/10
Before 4 years sum was (O + 9 x – 10 × 4) and average = (O + 9 x – 10 × 4) /10
equating, Y + 9 x = O + 9x – 40
Y = O – 40
Younger is 40 years younger than Old one.
2. at the time of marriage,a man was 6 years elder to his wife.12 years after their marriage his age is 6/5 times the age of his wife..what was wife's age at the time of marriage?
Solution:
at d time of marriage
women=x
men=x+6
after 12 years
women=x+12
men=x+18
accn to d ques (6/5)(x+12)=x+18
=>x=90-72=18
3. A father is three times as old as his son. After fifteen years the father will be twice as old as his son's age at that time. Hence the father's present age is
Solution:
let father age=x and son age=x then x=3x,
after 15 years father age is twice i.e., 2(x+15)=3x+15
2x+30=3x+15
x=15 then father age is 3x=3*5=45.
4. Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?
A. 1 year
B. 2 years
C. 25 years
D. Data inadequate
E. None of these
Solution:
Ans.D
The difference between R & Q and Q & T is same
R-Q=Q-T and R+T=50
so, Q=25 but Question is (R - Q) = ? but we don't know the age of R.
so answer is D data inadequate.
5. When Raja was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Raja’s brother is 6 years older than Raja and his mother is 3 years younger than his father, how old was Raja’s sister when Raja was born?
Solution:
F = B+32
M = S+25
B = R+6... So When Raja Born , his brother's age ll be B=6...
M = F-3
S = F-28
F = 6+32 = 38
S = 38-28 = 10
Ans : 10
6. A and B are 3 years 2 years old respectively.thier father is 40 years old.After how many years,father age would be the twice of combined age of Aand B?
Solution:
let after x years the age of the father is twice the combined age of A and B
A's age B'sage Fathers's age
initial age= 3 2 40
after x years= 3+x 2+x 40+x
then according to d ques
2*(3+x+2+x)=40+x
=>2*(5+2x)=40+x
=>10+4x=40+x
=>3x=30
=>x=10
(or)
condition F=2(A+B)
sub the year 10
it satisfise the condition
7. A wizard named Nepo says "I am only three times my son's age. My father is 40 years more than twice my age. Together the three of us
are a mere 1240 years old." How old is Nepo?
Solution:
let the age of nepo be x years,age of his father is (40+2x),age of his son (x/3)
(40+2x)+x+(x/3)=1240
solving this equation we get the age of nepo i.e.
(x) is 360 years old.
8. The sum of ages of suresh and his father is 46 years.3 years back father's age was 4 times suresh's age.find present age of suresh.
Soluton:
x is son y is father
x+y=46
y-3=4(x-3) =>y=4x-9
put value
4x-9+x=46
x=11,y=35
(or)
Let suresh age be s yrs and his fathers age be f yrs. By writing as equation
S+F=46 since sum of ages is 46
F-3=4(S-3) 3 yrs back their ages would be S-3 and F-3.
Solving both we get S=11,F=35
9. The sum of ages of suresh and his father is 78 years.6 years hence father's age will be twice of suresh's age.find present age of father.
Solution:
s+f=78
f+6=2(s+6)
f+6=2(78-f+6)
f+6=2(84-f)
f+2f=168-6
f=162/3=54
10. Total of the ages of A, B ahd C at present is 90 years. Ten years ago, the ratio of their ages was 1: 2: 3. What is the age of B at present.
Soluton:
A+B+C = 90
(A-10) : (B-10) : (C-10) => 1:2:3
Total age before 10 years = 90-30 = 60
A's age before 10 years = 60*1/(1+2+3) = 10
B' age before 10 years = 60*2/6 = 20
C' age before 10 years = 60*3/6 = 30
B's present age = 20+10 = 30
Ans : 30
(or)
A+B+C=90
THEN AGE OF B = 90*2/6=30
11. The age of the grand father is the sum of his three grandsons.The second is 2 year younger than first one and the third one is 2 year younger than the second one. Then what will be the age of the grandfather?
Solution:
let age of grandfather be x and the ages of the grandsons are y1,y2,y3 respectively
x= y1+y2+y3 where y2= y1-2 and y3 =y2 -2 =y1 -4
x=3y1 - 6= 3(y1-2)
x= 3y2
so age of grand father is three times the age of second grandson
12. Raju is 10 years elder to Sita. 10 years from now Raju would be twice as old as sita was before 10 years. How old would be Sita after 12 years.
Solution:
Sita's age=x
so,raju's age =x+10
by given condition,
x+10+10=2(x+10-10)
so x=20
sita's age after 12 yrs=20+12=32yrs.
13. Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?
A. 16 years
B. 18 years
C. 20 years
D. Cannot be determined
E. None of these
Solution:
ans.A
(x-6)/(y-6)=6/5
(x+4)/(y+4)=11/10
after solving we get y=16
14. A person is 80 years old in 490 and only 70 years old in 500 in which year is he born?
Solution:
80 years old in 490 or 70 years old in 500
year of birth= 500+70= 570 BC
15. Three years ago , the average age of A, B and C was 27 years and that of B and C, 5 years ago was 20 years. A’s present age is :
A) 30 yrs B) 35 yrs C) 40 yrs D)48 yrs
Solution:
Sum of the present ages of A, B and C = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of B and C = (20 x 2 + 5 x 2) years = 50 years.
A's present age = (90 - 50) years = 40 years.
16. The ratio of the present ages of Sunita and vinita is 4:5. Six years hence the ratio of their ages will be 14:17. What will be the ratio of their ages 12 years hence?
1) 15:19
2) 13:15
3) 16:19
4) 17:19
5) None of these
Solution:
present age sunita:vinita=4:5
lets their age is 4x and 5y respectively..
after 6 yrs their age ratio will be 14:17
therefore (4x+6)/(5x+6)=14/17
=>x=9
therefore their present age is 36,45 repectvely
after 12 yrs their age will be 48,57 respectively
=>ratio after 12 yrs will be 48/57=16/19=16:19
therefore ans is 16:19
17. When I add 3 times my age 3 years from now to 4 times my age 4 years from now, I get 8 times my current age. How old will I be 3 years from now?
A. 28 years
B. 24 years
C. 20 years
D. 32 years
E. 30 years
Solution:
let my age be x years now
3 years from now my age will be x+3
3 times age 3 years from now will be 3(x+3)
4 years from now my age will be x+4
4 times age 4 years from now will be 4(x+5)
8 times my age now = 8x
..
3(x+3)+4(x+4)=8x
7x+25 =8x
x=25
therefore three years from now he will be=25+3=28yrs
18. The average age of a woman and her daughter is 16 years. The ratio of their ages in 7 : 1 respectively. What is the woman’s age?
Solution:
The average age of a woman and her daughter is 16 years.
sum of ages = 16*2=32 years.
The ratio of their ages in 7 : 1 say 7x and x.
then 8x = 32
x=4
Then age of woman = 7x = 28 years
19. The ratio between A's and 13's ages two years ago was 3: 2 and at present it is 7: 5. Find B's present age ?
Solution:
A : B present = 7 : 5
A : B 2 years ago = 3 : 2
then B's present age = (5 *( 3 - 2 )*2) / 14 - 15 = 10 yrs
20. The ratio of the ages of A and B is 9:5. After 8 years B would reach the present age of A. Find the present ages of B and A respectively.
A. 9, 5
B. 10, 18
C. 18, 10
D. 5, 9
E. 5, 7
Solution:
B. 10, 18
Let the present ratio of A & B be 9x and 5x
According to the condition 5x+8=9x ->4x=8 or x=2
Therefore the present age of A=9*2=18 and B=5*2=10
21. Four years ago Rekha's mother was 2 3/4 times elder than her in age. If the total age of the two then was 60 yrs. what is the present age of Rekha ?
a. 24 yrs
b. 20 yrs
c. 16 yrs
d. 12 yrs
e. 8 yrs
Solution:
let age of rekha be x
x+2*3/4x=60
15/4x=60
x=16
present age =x+4=16+4=20
22. Father's age is three years more than three times the son's age. After three years, father's age will be ten years more than twice the son's age. What is the father's present age?
Solution:
Let the son's present age be x years.then father's present age will be 3x+3 years.
After 3 years,3x+3+3=2(x+3)+10
solving we get, x=10.
substituting x=10 in 3x+3,
hence father's present age will be x=33 years.
23. My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 140 years. Can you tell me my age in years?
Solution:
let the age of the man = x years
so according to the given condition
age of my grandson = x/12 years
and age of my son = x30/52 = 15x/26
and x + (x/12) + (15x/26) = 140
or (156x+13x+90x)/156 = 140
or 259x = 156*140
or x = 156*140/259 = 84 (approx)
24. A father's age was 5 times his son's age 5 years ago and will be 3 times son's age after 2 years, the ratio of their present ages is equal to:
Solution:
father=x
son=y
x-5=5(9y-5)
x+2=3(y+2)
solve x/y=10/3
25. When Rajeev was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Rajeev's brother is 6 years older than Rajeev and his mother is 3 years younger than his father, how old was Rajeev's sister when Rajeev was born?
Solution:
his brother is x years old
thn his father is 6+32=38 when rajeev was born
and his mother is 3 years yonger thn hi father so his mother was 35 years old whn rajeev was born
and his sister is 25 year younger thn his mother
so rajeev's sister was 10 years old when rajeev was born.
(or)
Rajeev 0years
brother 6 year
father=brother age+32years=6+32=38
mother=fathers age-3=35
so sister age=35-25=10years
26. the sum of the ages of a,b and c was 52 three years ago.Four years ago B,who is a year younger than C,was 1 1/2 times as old as A.The sum of the ages of B and C two years hence,will be
Solution:
Present sum of ages of a,b & c= a+b+c =52+9=61 ---(i)
Given b is a year younger than c, so b+1=c ---(ii)
Also b-4=(a-4)*3/2 or 2b -8=3a-12 or 2b -3a= -4 ---(iii)
Substituting c=b+1 from (ii) in (i), a+2b=60 ---(iv)
On solving (iii) & (iv), a=16, b=22 so c=23
So sum of the ages of b & c two year hence= (b+2)+(c+2)=24+25=49
27. The sum of the ages of abhigail,jennifer and margaret was 52 three year ago.four years ago,jennifer who is a year younger than margaret,was 3/2 times as old as abhigail.the sum of ages of jennifer and margaret two year hence will be?
Solution:
3 yrs ago sum = A+j+m=52
present ages sum= A+j+m=61
J=M-1 or M =J+1
J-4 =3/2(A-4)
A= (2 J+4)/3
Substitute all in Second eqn of Sum of present ages
(2j+4)/3 + j + j +1 =61
8j =176
j=22 present , m= 23 present
after 2 yrs sum = (22+2) +(23+2) =49
28. The ratio of the ages of aunt agatha and uncle Roger is 5:6, the same as the ratio of the ages of their children, Suzanne and Bemard. if the sum of the ages of Suzanne and aunt Agath, five years ago, was 60, what will be the sum of the ages of Bemard and uncle Roger five years, hence?
Solution:
Let ages of aunt nd auncle 5:6 ratio then ages are 5x nd 6x
In same way chldrn ages 5y nd 6y
So 5yrs ago aunt, suzn total
(5x-5)+(5y-5)=60 >> x+y=14
Then aftr 5yrs ancle,bemard age total
(6x+5)+(6y+5)=6(x+y)+10=94
29. Mr. Roy is twelve years more than twice the age of his son at present. After twelve years, he will be thrice as old as his son. What is the age of Mr.Roy at present?
Solution:
given data is wrong.
3(x+12)=2x+24
3x+36=2x+24
x= -36+24 = -12 which is not possible
30. the ratio of the ages of aunt agatha and uncle roger is 5:6,the same as the ratio of the ages of thier or their children,suzaman and beard.if the the sum of the ages of suzanne and aunt agatha,five years ago,was 60,what will be the sum of the ages of bernard and uncle roger five years hence?
Solution:
Aunt/uncle=5/6 Suzaan/beard=5/6
so aunt+suzaan=5x+5y
Before 5 years= 5(x+y)-10=60 x+y=14
again,
After 5 yrs, uncle+beard=
6(x+y)+5+5= 6(14)+10= 94.
31. A is 4 yrs old and B is thrice A>when A is 12 yrs, how old will B be?
Solution:
a=4
b=3*4=12
now age of a is 12yrs
i.e after 8 yrs..
b= 8+12=20
32. Rams Mather is 20 years more than twice his age.Total of their age is 35.What is Rams age?
Solution:
let x be the age of Ram and y be the age of her mother given 2x+20=y and 2x+20+y=35 , solve it u will get x=5 years
33. Total of ages of A,B and C at present is 90 years. If ratio of this ages is 2 : 3 : 4 what will be the age of C after 5 years?
Solution:
2x+3x+4x=90
=>x=10
c=40..after 5 years 40+5=45 years
34. The ratio of ages of A and B at present is 2:3. After five years the ratio of their ages will be 3:4 What is the present age of A in years?
Solution:
Present age ratio are: 2x 3x
after 5 years, (2x+5)/(3x+5)=3/4
x=5
A's age is= 10
35. When I was born, my mother was 23 years of age. After 6 years, when my sister was born, my father was 34 years of age. what is the difference between the ages of my parents?
Solution:
When age of Son=0 ,Mother=23
After 6 years, Son=6 ,Mother=23+6=29 ,Father=34
So difference between ages of Mother & Father=34-29=5
36. A man is three (3) years older than his wife and four (4) times as old as his son. If the son attains an age of fifteen (15) years after three (3) years, what is the present age of the mother?
Solution:
Let mother age be x
Father age be x+3
X+3=4×12
X=45
37. If the ratio of ages of two friends is 4:3 and sum of their ages is 70 years then what is the age of older friend?
Solution:
4x+3x=70 => x= 10
so 4*10 =40
38. At the time of marriage, a man was 6 years elder to his wife. 12 years after their marriage, his age is 6/5 times the age of his wife. What was wife's age at the time of marriage ?
Solution:
18 is correct
let wifes age= x
husband age = x+6
now after 12 years of mrg x+12 wifes age
x+6+12 husbands age
6/5(x+12)=x+6+12
after solving x=18
39. Sum of ages of father and his son is 60 years while difference is 30 years. what is father's age?
Solution:
F+s=60
F-s=30
by subsituting 2f=90. therefore f=45
40. 10 years ago Neha's mother was 4 times older than Neha. After 10 years Neha's mother will be twice Neha's age. How old is Neha now?
Solution:
Let us assume m = mother and n = neha
m-10 = 4(n-10) => 4n-m = 30 this is equation 1
m+10 = 2(n+10 => -2n+m = 10 this is equation 2
By equations 1 and 2
n=20
n means Neha age = 20 years
41. If the ratio of ages of Mohan and Rakesh 4:3 and sum of their ages is 28 years then ratio of their ages after 4 years will be
Solution:
let monhan age is 4x and rakesh age is 3x.
accn to d ques 4x+3x=7x
7x=28
x=4
after 4 years mohan will be 4x+4=(4*4)+4=20
rakesh will be=3x+4=(3*4)+4=16
20:16=5:4
(or)
4x+3x=28
7x=28
x=4
mohan=16+4=20
rakesh=12+4=16
ratio= 5:4
42. Fathers age is 5 times his son's age. 4 years back the father was 9 times older than son.Find the fathers' present age.
Solution:
fathers age =x sons age =y
x=5y;x-4=9(y-4)
5y-4=9y-36
y=8 so x=40
43. A boy is born when his father is 27 years old. How old will he be when he is exactly half his fathers' age?
Solution:
when son born:
son s=0
father f=27.
after x years:
son s=x
father f=f+x=27+x:
according to given condition
son age is exactly half his fathers' age...so
x=(27+x)/2---solve this
son age is 27
44. A father told his son "I was as old as you are at present, at the time of your birth". If the father is 38 years old now, then what was the son's age five years ago in years?
Solution:
let son's present age is =x
then 38-x=x
x=19
son's age 5 years back is 19-5=14 years.
45. My age is two year more than twice than of Ram. If I am 34 years old, how old is Ram?
Solution:
myage = 2 + 2*Ram
34 = 2 + 2*Ram
2(Ram) = 32
Ram = 16
46. The average age of Indira and Meena is 28 years. If Kala's age is added to it, then the average of the ages of the three becomes 27 years, what is kala's age?
Solution:
sum=28*2= 56
sum=27*3=81
81-56=25
47. A father tells his son, "I was of your present age when you were born." If the father is 36 now, how old was the boy 5 years back?
Solution:
present age of father 36
present age of son x
36-x=x
x=18
five yrs back sons age 18-5=13
48. 5 years ago Ashu's mother was three times as old as Ashu. After 5 years, she will be twice as old as Ashu. How old is ashu today?
Solution:
5 years ago::m- mother,a-ashu
m-5=3(a-5)......eq1
After 5 years
m+5=2(a+5)....eq2
By solving 1&2
a=15
So ashu age is 15 years
49. The ratio of ages of two friends is 3:5 and sum of their ages is 80 years. What are their present ages in years?
Solution:
3x + 5x== 80
x==10
(30,50)
50. Ten years ago A was half of B’s Age. If ratio of their present ages is 3:4 then what is the total of their present ages?
Solution:
present age of A= 3x
present age of B= 4x
10 years ago A was half of B's age
3x-10=1/2(4x-10)
2x=10
x=5
total of their present age
A=3x=3*5=15
B=4x=4*5=20
toatal present age=35yrs
51. The age of Ritu’s mother is 6 times that of Ritu’s age. After 6 years it will be 3 times that of Ritu’s age. what is Ritu’s present age?
Solution:
let us consider 'm' be the ritu's mom's age and 'r' be the ritu's present age
Given: m=6r ;
m+6=3(r+6);
6r+6=3r+18;
as we solve for r, we get ritu's age as 4 years.
52. The age of a father is 5/2 of his daughter. 5 years ago it was 3 times that of his daughter.what is daughter's present age?
Solution:
daughter's present age is x
father's present age is (5/2)*x
5 years ago father's age is (5x/2)-5=3(x-5)
Therefore,x=20 years
(or)
F=5/2(d)
F-5=3(d-5)
(5/2)d-5=3d-15
5d-10=6d-30
D=20
53. The average of a couple was 23Yrs when they were married 5Yrs ago.The avg age of the couple and a child, who was born during the interval, is 20Yrs now. How old is the child now ?
Solution:
(a+b-5-5)/2=23;
a+b=56;
a+b+c/3=20;
solving both c=4
54. Ratio of Ravi's and Ashok's present ages is 4:5 After 6 years it will be 5:6. What is Ravi's present age?
Solution:
Let present ages are 4x and 5x
After 6 years hence
4x+6/5x+6=5/6
After solving above eqn
X=6
So ravis present age become 4*6=24
55. The age of Ritu's mother is 6 times that of Ritu's age. After 6 years it will be 3 times that of Ritu's age. what is Ritu's present age?
Solution:
Let present age of Ritu=x
then, present age of ritu's mother=6x
A/c
after 6 years
=>6x+6=3(6+x)
x=4
so, Ritu present age is 4 years
Solution:
Let the members be Old Having age O + other 9 having ages x and New one having age Y
Sum of their ages = (Y + 9 × x) and average = (Y + 9 × x)/10
Before 4 years sum was (O + 9 x – 10 × 4) and average = (O + 9 x – 10 × 4) /10
equating, Y + 9 x = O + 9x – 40
Y = O – 40
Younger is 40 years younger than Old one.
2. at the time of marriage,a man was 6 years elder to his wife.12 years after their marriage his age is 6/5 times the age of his wife..what was wife's age at the time of marriage?
Solution:
at d time of marriage
women=x
men=x+6
after 12 years
women=x+12
men=x+18
accn to d ques (6/5)(x+12)=x+18
=>x=90-72=18
3. A father is three times as old as his son. After fifteen years the father will be twice as old as his son's age at that time. Hence the father's present age is
Solution:
let father age=x and son age=x then x=3x,
after 15 years father age is twice i.e., 2(x+15)=3x+15
2x+30=3x+15
x=15 then father age is 3x=3*5=45.
4. Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?
A. 1 year
B. 2 years
C. 25 years
D. Data inadequate
E. None of these
Solution:
Ans.D
The difference between R & Q and Q & T is same
R-Q=Q-T and R+T=50
so, Q=25 but Question is (R - Q) = ? but we don't know the age of R.
so answer is D data inadequate.
5. When Raja was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Raja’s brother is 6 years older than Raja and his mother is 3 years younger than his father, how old was Raja’s sister when Raja was born?
Solution:
F = B+32
M = S+25
B = R+6... So When Raja Born , his brother's age ll be B=6...
M = F-3
S = F-28
F = 6+32 = 38
S = 38-28 = 10
Ans : 10
6. A and B are 3 years 2 years old respectively.thier father is 40 years old.After how many years,father age would be the twice of combined age of Aand B?
Solution:
let after x years the age of the father is twice the combined age of A and B
A's age B'sage Fathers's age
initial age= 3 2 40
after x years= 3+x 2+x 40+x
then according to d ques
2*(3+x+2+x)=40+x
=>2*(5+2x)=40+x
=>10+4x=40+x
=>3x=30
=>x=10
(or)
condition F=2(A+B)
sub the year 10
it satisfise the condition
7. A wizard named Nepo says "I am only three times my son's age. My father is 40 years more than twice my age. Together the three of us
are a mere 1240 years old." How old is Nepo?
Solution:
let the age of nepo be x years,age of his father is (40+2x),age of his son (x/3)
(40+2x)+x+(x/3)=1240
solving this equation we get the age of nepo i.e.
(x) is 360 years old.
8. The sum of ages of suresh and his father is 46 years.3 years back father's age was 4 times suresh's age.find present age of suresh.
Soluton:
x is son y is father
x+y=46
y-3=4(x-3) =>y=4x-9
put value
4x-9+x=46
x=11,y=35
(or)
Let suresh age be s yrs and his fathers age be f yrs. By writing as equation
S+F=46 since sum of ages is 46
F-3=4(S-3) 3 yrs back their ages would be S-3 and F-3.
Solving both we get S=11,F=35
9. The sum of ages of suresh and his father is 78 years.6 years hence father's age will be twice of suresh's age.find present age of father.
Solution:
s+f=78
f+6=2(s+6)
f+6=2(78-f+6)
f+6=2(84-f)
f+2f=168-6
f=162/3=54
10. Total of the ages of A, B ahd C at present is 90 years. Ten years ago, the ratio of their ages was 1: 2: 3. What is the age of B at present.
Soluton:
A+B+C = 90
(A-10) : (B-10) : (C-10) => 1:2:3
Total age before 10 years = 90-30 = 60
A's age before 10 years = 60*1/(1+2+3) = 10
B' age before 10 years = 60*2/6 = 20
C' age before 10 years = 60*3/6 = 30
B's present age = 20+10 = 30
Ans : 30
(or)
A+B+C=90
THEN AGE OF B = 90*2/6=30
11. The age of the grand father is the sum of his three grandsons.The second is 2 year younger than first one and the third one is 2 year younger than the second one. Then what will be the age of the grandfather?
Solution:
let age of grandfather be x and the ages of the grandsons are y1,y2,y3 respectively
x= y1+y2+y3 where y2= y1-2 and y3 =y2 -2 =y1 -4
x=3y1 - 6= 3(y1-2)
x= 3y2
so age of grand father is three times the age of second grandson
12. Raju is 10 years elder to Sita. 10 years from now Raju would be twice as old as sita was before 10 years. How old would be Sita after 12 years.
Solution:
Sita's age=x
so,raju's age =x+10
by given condition,
x+10+10=2(x+10-10)
so x=20
sita's age after 12 yrs=20+12=32yrs.
13. Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?
A. 16 years
B. 18 years
C. 20 years
D. Cannot be determined
E. None of these
Solution:
ans.A
(x-6)/(y-6)=6/5
(x+4)/(y+4)=11/10
after solving we get y=16
14. A person is 80 years old in 490 and only 70 years old in 500 in which year is he born?
Solution:
80 years old in 490 or 70 years old in 500
year of birth= 500+70= 570 BC
15. Three years ago , the average age of A, B and C was 27 years and that of B and C, 5 years ago was 20 years. A’s present age is :
A) 30 yrs B) 35 yrs C) 40 yrs D)48 yrs
Solution:
Sum of the present ages of A, B and C = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of B and C = (20 x 2 + 5 x 2) years = 50 years.
A's present age = (90 - 50) years = 40 years.
16. The ratio of the present ages of Sunita and vinita is 4:5. Six years hence the ratio of their ages will be 14:17. What will be the ratio of their ages 12 years hence?
1) 15:19
2) 13:15
3) 16:19
4) 17:19
5) None of these
Solution:
present age sunita:vinita=4:5
lets their age is 4x and 5y respectively..
after 6 yrs their age ratio will be 14:17
therefore (4x+6)/(5x+6)=14/17
=>x=9
therefore their present age is 36,45 repectvely
after 12 yrs their age will be 48,57 respectively
=>ratio after 12 yrs will be 48/57=16/19=16:19
therefore ans is 16:19
17. When I add 3 times my age 3 years from now to 4 times my age 4 years from now, I get 8 times my current age. How old will I be 3 years from now?
A. 28 years
B. 24 years
C. 20 years
D. 32 years
E. 30 years
Solution:
let my age be x years now
3 years from now my age will be x+3
3 times age 3 years from now will be 3(x+3)
4 years from now my age will be x+4
4 times age 4 years from now will be 4(x+5)
8 times my age now = 8x
..
3(x+3)+4(x+4)=8x
7x+25 =8x
x=25
therefore three years from now he will be=25+3=28yrs
18. The average age of a woman and her daughter is 16 years. The ratio of their ages in 7 : 1 respectively. What is the woman’s age?
Solution:
The average age of a woman and her daughter is 16 years.
sum of ages = 16*2=32 years.
The ratio of their ages in 7 : 1 say 7x and x.
then 8x = 32
x=4
Then age of woman = 7x = 28 years
19. The ratio between A's and 13's ages two years ago was 3: 2 and at present it is 7: 5. Find B's present age ?
Solution:
A : B present = 7 : 5
A : B 2 years ago = 3 : 2
then B's present age = (5 *( 3 - 2 )*2) / 14 - 15 = 10 yrs
20. The ratio of the ages of A and B is 9:5. After 8 years B would reach the present age of A. Find the present ages of B and A respectively.
A. 9, 5
B. 10, 18
C. 18, 10
D. 5, 9
E. 5, 7
Solution:
B. 10, 18
Let the present ratio of A & B be 9x and 5x
According to the condition 5x+8=9x ->4x=8 or x=2
Therefore the present age of A=9*2=18 and B=5*2=10
21. Four years ago Rekha's mother was 2 3/4 times elder than her in age. If the total age of the two then was 60 yrs. what is the present age of Rekha ?
a. 24 yrs
b. 20 yrs
c. 16 yrs
d. 12 yrs
e. 8 yrs
Solution:
let age of rekha be x
x+2*3/4x=60
15/4x=60
x=16
present age =x+4=16+4=20
22. Father's age is three years more than three times the son's age. After three years, father's age will be ten years more than twice the son's age. What is the father's present age?
Solution:
Let the son's present age be x years.then father's present age will be 3x+3 years.
After 3 years,3x+3+3=2(x+3)+10
solving we get, x=10.
substituting x=10 in 3x+3,
hence father's present age will be x=33 years.
23. My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 140 years. Can you tell me my age in years?
Solution:
let the age of the man = x years
so according to the given condition
age of my grandson = x/12 years
and age of my son = x30/52 = 15x/26
and x + (x/12) + (15x/26) = 140
or (156x+13x+90x)/156 = 140
or 259x = 156*140
or x = 156*140/259 = 84 (approx)
24. A father's age was 5 times his son's age 5 years ago and will be 3 times son's age after 2 years, the ratio of their present ages is equal to:
Solution:
father=x
son=y
x-5=5(9y-5)
x+2=3(y+2)
solve x/y=10/3
25. When Rajeev was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Rajeev's brother is 6 years older than Rajeev and his mother is 3 years younger than his father, how old was Rajeev's sister when Rajeev was born?
Solution:
his brother is x years old
thn his father is 6+32=38 when rajeev was born
and his mother is 3 years yonger thn hi father so his mother was 35 years old whn rajeev was born
and his sister is 25 year younger thn his mother
so rajeev's sister was 10 years old when rajeev was born.
(or)
Rajeev 0years
brother 6 year
father=brother age+32years=6+32=38
mother=fathers age-3=35
so sister age=35-25=10years
26. the sum of the ages of a,b and c was 52 three years ago.Four years ago B,who is a year younger than C,was 1 1/2 times as old as A.The sum of the ages of B and C two years hence,will be
Solution:
Present sum of ages of a,b & c= a+b+c =52+9=61 ---(i)
Given b is a year younger than c, so b+1=c ---(ii)
Also b-4=(a-4)*3/2 or 2b -8=3a-12 or 2b -3a= -4 ---(iii)
Substituting c=b+1 from (ii) in (i), a+2b=60 ---(iv)
On solving (iii) & (iv), a=16, b=22 so c=23
So sum of the ages of b & c two year hence= (b+2)+(c+2)=24+25=49
27. The sum of the ages of abhigail,jennifer and margaret was 52 three year ago.four years ago,jennifer who is a year younger than margaret,was 3/2 times as old as abhigail.the sum of ages of jennifer and margaret two year hence will be?
Solution:
3 yrs ago sum = A+j+m=52
present ages sum= A+j+m=61
J=M-1 or M =J+1
J-4 =3/2(A-4)
A= (2 J+4)/3
Substitute all in Second eqn of Sum of present ages
(2j+4)/3 + j + j +1 =61
8j =176
j=22 present , m= 23 present
after 2 yrs sum = (22+2) +(23+2) =49
28. The ratio of the ages of aunt agatha and uncle Roger is 5:6, the same as the ratio of the ages of their children, Suzanne and Bemard. if the sum of the ages of Suzanne and aunt Agath, five years ago, was 60, what will be the sum of the ages of Bemard and uncle Roger five years, hence?
Solution:
Let ages of aunt nd auncle 5:6 ratio then ages are 5x nd 6x
In same way chldrn ages 5y nd 6y
So 5yrs ago aunt, suzn total
(5x-5)+(5y-5)=60 >> x+y=14
Then aftr 5yrs ancle,bemard age total
(6x+5)+(6y+5)=6(x+y)+10=94
29. Mr. Roy is twelve years more than twice the age of his son at present. After twelve years, he will be thrice as old as his son. What is the age of Mr.Roy at present?
Solution:
given data is wrong.
3(x+12)=2x+24
3x+36=2x+24
x= -36+24 = -12 which is not possible
30. the ratio of the ages of aunt agatha and uncle roger is 5:6,the same as the ratio of the ages of thier or their children,suzaman and beard.if the the sum of the ages of suzanne and aunt agatha,five years ago,was 60,what will be the sum of the ages of bernard and uncle roger five years hence?
Solution:
Aunt/uncle=5/6 Suzaan/beard=5/6
so aunt+suzaan=5x+5y
Before 5 years= 5(x+y)-10=60 x+y=14
again,
After 5 yrs, uncle+beard=
6(x+y)+5+5= 6(14)+10= 94.
31. A is 4 yrs old and B is thrice A>when A is 12 yrs, how old will B be?
Solution:
a=4
b=3*4=12
now age of a is 12yrs
i.e after 8 yrs..
b= 8+12=20
32. Rams Mather is 20 years more than twice his age.Total of their age is 35.What is Rams age?
Solution:
let x be the age of Ram and y be the age of her mother given 2x+20=y and 2x+20+y=35 , solve it u will get x=5 years
33. Total of ages of A,B and C at present is 90 years. If ratio of this ages is 2 : 3 : 4 what will be the age of C after 5 years?
Solution:
2x+3x+4x=90
=>x=10
c=40..after 5 years 40+5=45 years
34. The ratio of ages of A and B at present is 2:3. After five years the ratio of their ages will be 3:4 What is the present age of A in years?
Solution:
Present age ratio are: 2x 3x
after 5 years, (2x+5)/(3x+5)=3/4
x=5
A's age is= 10
35. When I was born, my mother was 23 years of age. After 6 years, when my sister was born, my father was 34 years of age. what is the difference between the ages of my parents?
Solution:
When age of Son=0 ,Mother=23
After 6 years, Son=6 ,Mother=23+6=29 ,Father=34
So difference between ages of Mother & Father=34-29=5
36. A man is three (3) years older than his wife and four (4) times as old as his son. If the son attains an age of fifteen (15) years after three (3) years, what is the present age of the mother?
Solution:
Let mother age be x
Father age be x+3
X+3=4×12
X=45
37. If the ratio of ages of two friends is 4:3 and sum of their ages is 70 years then what is the age of older friend?
Solution:
4x+3x=70 => x= 10
so 4*10 =40
38. At the time of marriage, a man was 6 years elder to his wife. 12 years after their marriage, his age is 6/5 times the age of his wife. What was wife's age at the time of marriage ?
Solution:
18 is correct
let wifes age= x
husband age = x+6
now after 12 years of mrg x+12 wifes age
x+6+12 husbands age
6/5(x+12)=x+6+12
after solving x=18
39. Sum of ages of father and his son is 60 years while difference is 30 years. what is father's age?
Solution:
F+s=60
F-s=30
by subsituting 2f=90. therefore f=45
40. 10 years ago Neha's mother was 4 times older than Neha. After 10 years Neha's mother will be twice Neha's age. How old is Neha now?
Solution:
Let us assume m = mother and n = neha
m-10 = 4(n-10) => 4n-m = 30 this is equation 1
m+10 = 2(n+10 => -2n+m = 10 this is equation 2
By equations 1 and 2
n=20
n means Neha age = 20 years
41. If the ratio of ages of Mohan and Rakesh 4:3 and sum of their ages is 28 years then ratio of their ages after 4 years will be
Solution:
let monhan age is 4x and rakesh age is 3x.
accn to d ques 4x+3x=7x
7x=28
x=4
after 4 years mohan will be 4x+4=(4*4)+4=20
rakesh will be=3x+4=(3*4)+4=16
20:16=5:4
(or)
4x+3x=28
7x=28
x=4
mohan=16+4=20
rakesh=12+4=16
ratio= 5:4
42. Fathers age is 5 times his son's age. 4 years back the father was 9 times older than son.Find the fathers' present age.
Solution:
fathers age =x sons age =y
x=5y;x-4=9(y-4)
5y-4=9y-36
y=8 so x=40
43. A boy is born when his father is 27 years old. How old will he be when he is exactly half his fathers' age?
Solution:
when son born:
son s=0
father f=27.
after x years:
son s=x
father f=f+x=27+x:
according to given condition
son age is exactly half his fathers' age...so
x=(27+x)/2---solve this
son age is 27
44. A father told his son "I was as old as you are at present, at the time of your birth". If the father is 38 years old now, then what was the son's age five years ago in years?
Solution:
let son's present age is =x
then 38-x=x
x=19
son's age 5 years back is 19-5=14 years.
45. My age is two year more than twice than of Ram. If I am 34 years old, how old is Ram?
Solution:
myage = 2 + 2*Ram
34 = 2 + 2*Ram
2(Ram) = 32
Ram = 16
46. The average age of Indira and Meena is 28 years. If Kala's age is added to it, then the average of the ages of the three becomes 27 years, what is kala's age?
Solution:
sum=28*2= 56
sum=27*3=81
81-56=25
47. A father tells his son, "I was of your present age when you were born." If the father is 36 now, how old was the boy 5 years back?
Solution:
present age of father 36
present age of son x
36-x=x
x=18
five yrs back sons age 18-5=13
48. 5 years ago Ashu's mother was three times as old as Ashu. After 5 years, she will be twice as old as Ashu. How old is ashu today?
Solution:
5 years ago::m- mother,a-ashu
m-5=3(a-5)......eq1
After 5 years
m+5=2(a+5)....eq2
By solving 1&2
a=15
So ashu age is 15 years
49. The ratio of ages of two friends is 3:5 and sum of their ages is 80 years. What are their present ages in years?
Solution:
3x + 5x== 80
x==10
(30,50)
50. Ten years ago A was half of B’s Age. If ratio of their present ages is 3:4 then what is the total of their present ages?
Solution:
present age of A= 3x
present age of B= 4x
10 years ago A was half of B's age
3x-10=1/2(4x-10)
2x=10
x=5
total of their present age
A=3x=3*5=15
B=4x=4*5=20
toatal present age=35yrs
51. The age of Ritu’s mother is 6 times that of Ritu’s age. After 6 years it will be 3 times that of Ritu’s age. what is Ritu’s present age?
Solution:
let us consider 'm' be the ritu's mom's age and 'r' be the ritu's present age
Given: m=6r ;
m+6=3(r+6);
6r+6=3r+18;
as we solve for r, we get ritu's age as 4 years.
52. The age of a father is 5/2 of his daughter. 5 years ago it was 3 times that of his daughter.what is daughter's present age?
Solution:
daughter's present age is x
father's present age is (5/2)*x
5 years ago father's age is (5x/2)-5=3(x-5)
Therefore,x=20 years
(or)
F=5/2(d)
F-5=3(d-5)
(5/2)d-5=3d-15
5d-10=6d-30
D=20
53. The average of a couple was 23Yrs when they were married 5Yrs ago.The avg age of the couple and a child, who was born during the interval, is 20Yrs now. How old is the child now ?
Solution:
(a+b-5-5)/2=23;
a+b=56;
a+b+c/3=20;
solving both c=4
54. Ratio of Ravi's and Ashok's present ages is 4:5 After 6 years it will be 5:6. What is Ravi's present age?
Solution:
Let present ages are 4x and 5x
After 6 years hence
4x+6/5x+6=5/6
After solving above eqn
X=6
So ravis present age become 4*6=24
55. The age of Ritu's mother is 6 times that of Ritu's age. After 6 years it will be 3 times that of Ritu's age. what is Ritu's present age?
Solution:
Let present age of Ritu=x
then, present age of ritu's mother=6x
A/c
after 6 years
=>6x+6=3(6+x)
x=4
so, Ritu present age is 4 years
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