1. A bag Contains 1,2,5 Rs coins in ratio 4:8:5 and total amount of 90.Rs. how many 5.Rs coins are there in that bag ?
Solution:
Ration is 4:8:5 .
Total amount in 1 Rupee coin is = Rs. 4x*1
Total amount in 2 Rupee coin is = Rs. 8x*2
Total amount in 5 Rupee coin is = Rs. 5x*5
So, 4x+16x+25x = 90; x=2
So no. of 5 rupee coin is = 5x = 10.
(or)
4x*1+8x*2+5x*5=90(coz given ratio is 4:8:5)
45x=90
x=2
So no. of 5 rupee coin is = 5x = 10
2. More than half of the members of a club are ladies.If 4/7 of the ladies and 7/11 of the gents in the club attended the meeting,then what is the smallest number that club could have?
Solution:
it would be 25 in smallest form , as for every 7 women 4 attended the meeting so for this ratio we can assume women to be (2*4/2*7) = (8/14) like there are 8 women attended the meeting from 14 women ,and for every 11 men 7 attended the meeting ,
so overall ( as per condition women are more than half of total members so we can say there are 11 men and 14 women ,as 14 women > 11 men )
i.e 11 men + 14 women gives 25 members for the club.
3. Three person Anil, Ram and Rishi whose salary together amounts to Rs. 81,000 spends 80%, 85% and 75% of their salaries respectively. If their savings are in the ratio of 8 : 9 : 20, find the salary of Ram.
Solution:
1/5x = 8 ---> x = 40
3/20y = 9 ---> y = 60
1/4z = 20 ---> z= 80
Ratio of their salary's = 40 : 60 : 80 = 2 : 3 : 4
Ram's salary = 3/9 × 81000 = 27000
4. steward assign 1/8th of his monthly salary for food.stewards total food bill for the month is rs.6500.what is stewards yearly salary?
Solution:
let steward monthly sal=x
1/8*x=6500=>x=6500*8=52000(total 1 month sal),
but given there his yearly sal=12*52000=624000
(or)
stewards total one month salary is
8*6500 = 52000
so his one year salary is 52000*12
which is 624000
5. The least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ratio less than 16 : 21, is?
Solution:
(6 - x) / (7 - x) < 16/21
=> 21 (6 - x) < 16 (7 - x)
=> 5x > 14
=> x > 2.8
So, Answer is 3.
6. A Product is supported each week by the same three customer service Representatives (CSR's). Last month the first CSR took 450 calls, the second took 350 calls, and the third took 300 calls. This month the job will consists of 1500 calls. If the three CSR's each increase their work proportionately, how many more calls will the first CSR take this month than last month?
Solution:
Last month ratio C1 : C2 : C3 = 45 : 35 : 30 => 9 : 7 : 6
This month total calls = 1500
9x + 7x + 6x = 1500
x= 1500/22 = 750/11
C1 ratio = 9 * 750/11 = 613.6 => 614 approximately
C2 ratio = 7 * 750/11 = 477.2
C3 ratio = 6 * 750/11 = 409
Calls first CSR ll take more than last month = 614 - 450 = 164
7. A started a business investing Rs 10,000. B joined him after six months with an amount of Rs 8,000 and C joined them with Rs 12,000 after another six months. The amount of profit earned should be distributed in what ratio among A, B and C respectively, four years after A started the business?
Solution:
A started the bussiness with investment 10000 for 4 years ie 48 months
B joined A after 6 months with investnemt 8000 for 3 years and 6 months i.e 42 months
c joined them after another six months i.e 1 year with an investment 12000for 3 years i.e for 36 months
By taking the ratio of 3 of the m we get
10000*48:8000*42:12000*36
=10:7:9
the profit is distributed in the ratio 10:7:9
8. Three partners Rahul, Nayan and Pooja together started a business. Twice the investment of Rahul is equal to thrice the capital of Nayan and the capital of Nayan is four times the capital of Pooja. Find the share of Nayan out of a profit Rs. 22275.
Solution:
let R , N,P be an investment of Rahul Nayan and pooja respectively
Therefore , 2R=3N ( given twice the investment of Rahul is equal to thrice the capital of Nayan) and
N=4P , now ratio of investment of N:R:P = 3N/2 : N :N/4
which is 6:4:1
therefore share of Mayan out of the profit of Rs 22275 = 4/11*22275 = 8100
9. Ramesh, xyz and Rajeev put a partnership. profit is 36000, if Ramesh and xyz ratio is 5 : 4 and xyz and Rajeev 8:9. Find Rajeev's share.
Solution:
ramesh:xyz=5:4
xyz:rajeev=8:9
ramesh:xyz:rajeev=10:8:9
rajeev=(36000*9)/27=12000
10. If 7:13::301:x then the value of ‘x’ is:
Solution:
Given the question;
7:13::301:x
7/13 = 301/x
7x = 301*13
x = 301*13/7
x = 559
11. a man buys a spirit at rs60/litre,adds water to it and then sells it at RS75/litre.what is the ratio of spirit to water if his profit in the deal is 75%
Solution:
c.p of spirit is 60/lit
s.p of 1 lit of mixture is 75
gain 75%
c.p of 1 lit of mixtre=(100/175)*75=300/7
by rule of aligation (60-300/7)/(300/7)=5:2
12. Rs 50000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 7000 Find money given by 10%?
Solution:
let x was given to a with 10% interest.
then b got 50,000 - x
interest = p*t*r /100
so
7000 =((50000 - x)*1*20)/100 +(x*1*10)/100
700000 = 1000000 - 10x
x = 30000
13. A rail network consist of 68 routes touching station A, B, C. 5 routes touches each of the three station. 2 routes touches B, C; 3 route touches B, A. 4 Route touches A, C. The ratio of route touching the A:B:C are 11:15:8. Find out how many route touches A, B, C, only. Find out also how many route touches A, B, C station?
Solution:
Given ratio as A : B : C = 11:15:8
Total routes for A = 68(11/34)= 22
A only = 22-3-5-4=10
Similarly total routes for B= 68(15/34)=30
B only = 30-3-5-2=10
Total routes for C= 68(8/34)= 16
C only = 16-4-5-2= 5
Number of routes touches A B C Only = 10+20+5=35
All routes of A B C Is= 22+30+16= 68
14. A milk seller buys milk at Rs 10 per litre and sells it at the same rate and makes a profit of 10% by adding water to it. How much water does he add to a litre of milk?
Solution:
100 ml
just do it by alligation and mixure....... cost price is (100/110)*10=>100/11.
now 0 10
100/11
10-100/11 : 100/11
ratio will be 1:10
15. The ratio of white balls and black balls is 1:2. If 9 gray balls is added it becomes 2:4:3. Then what is number of black balls ?
Solution:
3x=9
=>x=3
now white balls=2*3=6
black balls=4*3=12
so ratio of white and blak balls=1:2(proved)
blk balls=12
16. Find in what ratio will the total wages of the workers of a factory be increased or decreased. If there be a reduction in the ratio 15:11, and a increment in the wages in the ratio 22:25
Solution:
reduction in wage is =15:11
increment in wage is= 22:25
total wages ratio = reduction workers ratio* increment wage ratio
=(15/11)*(22/25)=6/5
total wages ratio =6/5
17. If the ratio of prod of 3 diff comp’s A B & C is 4:7:5 and of overall prod last yr was 4lac tones and if each comp had an increase of 20% in prod level this yr what is the prod of Comp B this yr?
Solution:
If the ratio of prod of 3 diff comp’s A B & C is 4:7:5 and of overall prod last yr was 4lac tones , then
prod of B last year = 4*7/16 = 7/4 lac tonnes
prod of B this year = 1.2*7/4 = 2.1 lac tonnes
18. Anirudh, Harish and Sahil invested a total of Rs.1,35,000 in the ratio 5:6:4 Anirudh invested has capital for 8 months. Harish invested for 6 months and Sahil invested for 4 months. If they earn a profit of Rs.75,900,then what is the share of Sahil in the profit?
Solution:
Total units={(5*8)+(6*6)+(4*4)}
=92.
sahil profit={16/92}75,900.
=13,200.
(or)
given ratio=5:6:4
Anirudh invest for 8 months,haris 4 6months and sahil for 4 months
so ratio =5*8 : 6*6 : 4*4
=40:36:16
=10:9:4
sahil's profit=(4/23)*75900
=13200
19. In what proportional should milk and water be mixed to reduce the cost of litre of milk from Rs 18 to Rs 16?
Solution:
Let total milk be x
now,
x milk costs Rs 18
so Rs 16 will have 8x/9 l milk
(unitary method)
means remaining part is water
so x-8x/9=x/9
now ratio is 8:1
20. Rs 5000 was divided among 5 men, 6 women and 5 boys, such that the ratio of the shares of men, women and boys is 5:3:2 what is the share of the boy?
Solution:
Given that ratio is 5:3:2.
Now the share of all boys will be (2/10)*5000=1000
So share of each boy will be: 1000/5=200
(or)
5x+3x+2x = 5000
x = 500
then
5 boys share = 2*500
then share of each boy = 2*500/5 = > 200
21. The sides of the triangle are in the ratio 1/2:1/3:1/5 and Its perimeter is 155 cm, what is the difference between the largest sides?
Solution:
Ratio of sides 1/2 : 1/3 : 1/5 =15 : 10 : 6
Given perimeter=155 cm , so if sides are 15x, 10x & 6x, then 15x+10x+6x =155 ,x=5
So side are 15*5=75 ,10*5=50 & 6*5=30 cm and
Difference between largest & smallest side=75 -30=45 cm
22. Kamal started a business investing Rs 9000. After five months, Sameer joined with a capital of Rs 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit ?
Solution:
Ratio of their investment => 9000 : 8000 => 9:8
Kamal's share's calculated for 12 months nd sameer's share calculated for (12-5) months...
Kamal : sameer => 9*12 : 8*7 => 108:56 => 27:14
Kamal's share = 6970*27/(27+14) = 4590
Sameer's share = 6970*14/41 = 2380
(or)
Kamal invested for 12 months and Sameer invested for 7 months.
So
Kamal:Sameer = (9000*12):(8000*7)
= 108:56
= 27:14
Sameer Ratio in profit will be
= (6970*14/41)
= Rs 2380
23. 2 vessels filled with pire contents.v1 contains 20Liter of milk v 2 contains 20 liter of water. 5 liter of milk is taken from v1 and rplaced in v2. then 4 liter of mixture is transferred from v2 to v1. find the ratio of water in v1 amount of milk in v2
Solution:
vessel m w
v1 20 0
v2 0 20
after first transfer
v1 15 0
v2 5 20
ratio of milk to water in v2 is 1:4
for 4 ltrs mixture 4/5 ltrs is milk,16/5ltrs is water
on next trnsfer
v1 15+4/5 16/5
v2 5-4/5 20-16/5
now ratio of water in v1 to milk in v2 is
(16/5)/(5-4/5)=16/21
24. There r three coins of Re 1, 50 ps, 25 ps having ratio of 13:11:3. the total sum of money is 77, then find out hw mny re. 1 coins is there?
Solution:
There r three coins of Re 1, 50 ps, 25 ps having ratio of 13:11:3.
if There r three coins of Re 1, 50 ps, 25 ps . No of coins are 13x,11x and 3x respectively..
Then
13x + 11x/2 + 3x/4 =77
x = 77*8/ (104+44+6)
= 77*8/154 = 4.
so no of 1 rupee coins
= 13x = 13*4= 52 coins.
25. A person has with him a certain number of weighing stones of 100gm, 500gm and 1 kg in the ratio of 3:5:1. If a maximum of 5 kg can be measured using weighing stones of 500gm alone, then what is the number of 100 gm stones he has?
Solution:
Number of 500gm stones
= 5kg/500gm = 10
Ratio = 3:5:1 or 6:10:2
Thus no. of 100gm stones
= 6
26. An alloy of zinc and copper contains the metals in the ratio 5 : 3. The quantity of zinc to be added to 16 kg of the alloy so that the ratio of the metal may be 3 : 1 is:
Solution:
5/8*16=10
3/8*16=6
(10+x)/6=3/1
=8 kg
27. Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
Solution:
let 100% seats are there in all then mathematics increased by 40% then
5*140/100=7
physics is increased by 50% then
7*150/100=21/2
biology increased by 75% then
8*175/100=14
then ratios of increasing seats are 7:21/2:14
14:21:28
2:3:4 is ans
28. A gets Rs.33 when a sum of money was distributed among A, B and C in the ratio 3:2:5 What will be the sum of money?
Solution:
total units=3+2+5=10
A's amount=33
let total = x
so according to d prb
(3/10) * x= 33
x=(33*10)/3
x=110
29. A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio of milk and water in the resultant mixture?
Solution:
Initially ixture has milk and water in ratio of 12:8.
when 10 ltr of mixture is removed , left mixture has milk and water in qnty/ratio of 6:4.
when 10 ltr milk is added , ratio becomes, 16:4, ratio is now 4:1
now milk is 8 lt and water is 2 lt in 10 lt mixture
again replaced by 10 lt of milk hence milk and water is in 18:2 in 20 lt mix
so ratio becomes 9:1
30. The proportion of milk and water in 3 samples is 2:1, 3:2 and 5:3. A mixture comprising of equal quantities of all 3 samples is made. The proportion of milk and water in the mixture is
Solution:
Proportion of milk in 3 samples is 2/3, 3/5, 5/8.
Proportion of water in 3 samples is 1/3, 2/5, 3/8.
Since equal quantities are taken,
Total proportion of milk is 2/3 + 3/5 + 5/8 = 227/120
Total proportion of water is 1/3 + 2/5 + 3/8 = 133/120
Proportion of milk and water in the solution is 227:133
31. An alloy of zinc and copper contains the metals in the ratio 5 : 3. The quantity of zinc to be added to 6 kg of the alloy so that the ratio of the metal may be 3 : 1 is:
Solution:
in 6kg of alloy 15/4-zinc and 9/4-copper .
so,
let extra zinc added be x
(15/4+x)/(9/4)=3/1
x=3
32. It has 20L mixutre conatins milk and water in the ratio 3:5,replace 4 litres of mixture with 4 litres of water what is the final ratio of milk and water.
Solution:
Full mixture has 7.5L milk 12.5L water if we fetch 4L mixture according to ratio it will be 1.5L milk & 2.5L water,replace this mixture from the water then it will be 6L milk and 14L water then ratio will be
6/14=3:7
(or)
Quantity of water in 16L of mix=16*(5/8)=10L
Quantity of water in 20L of new mix=(10+4)L
Quantity of milk in new mix=20-14=6L
then ratio=6/14=3:7
33. 729 ml of a mixture contains milk and water in ratio 7:2. How much of the water is to be added to get a new mixture containing half milk and half water?
Solution:
milk=(7/9)*729=567
water=(2/9)*729=162
according to question let z ml of water is added of mixture so
(729+z)*(50/100)=162+z
on solving
z=405 ml
34. In a theatre the ratio of car & two wheeler is 1:8. Total Number of tyres are 100. Find how many are cars and how many are two wheelers?
Solution:
let the no of cars be 1x and no of two wheelers be 8x
(1x*4)+(8x*2)=100
20x=100 ...x=5
1x=no of cars=5
8x=no of two wheelers=40
35. Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?
Solution:
simran=50k*3=150k
nanda=80k*2.5=200k
ratio=150k/200k=3:4
simran=3/7*24500=10500
36. A 20 litre solution conatins oil and kerosene in the ratio 3:5,replace 4 litres of mixture with 4 litres of kerosene what will be the ratio of oil and kerosene?
Solution:
When 4 liters are taken out of 20ml, amount of oil in remaining
16 lt = 3/8 * 16 = 6
Hence the remaining 10 litres would be kerosene
Now additional 4 litres of kerosene is added to the solution
So total quantity of kerosene = 14 litres
Ratio of oil:kerosene
= 6/14
= 3/7
37. It has 20 mixutre conatins mil and water in the ratio 3:5,replace 4 litres of mixture with 4 litres of water what is the final ratio of milk and water.
Solution:
the total mixture quantity=20 litre.
so,milk = 20*(3/8)=7.5
water = 12.5 (20-7.5)
when 4 litre removed,water and milk will become less in same ratio
milk = 7.5 - (4*3/8) = 6 litre
water = 12.5 - (4*5/8) = 10 litre
when 4 litre water added ,
water amount = 10+4 = 14.
ratio = 6/14 = 3/7
38. A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:
Solution:
Given that B has missed 27 times, means he attempted 54 shots..
but A fires 5 shots to B's 3
so A fires 90 shots to B's 54.
but A kills only once in 3 shots...
so
A has killed 30 Birds
(or)
Let the total no. of shots = x
shots fired by A = 5x/8;
shots fired by B= 3x/8;
killed by A= 1/3 of 5x/8= 5x/24;
missed by B= 1/2 of 3x/8= 3x/16;
A.T.Q :- 3x/16=27;
or x= 144;
so A has kiled= 5x/24= (5*144)/24= 30.
39. If A and B get profits of Rs. 6000 and Rs. 4000 respectively at the end of year the ratio of their investments are
Solution:
profit=Investment * Time
so,
6000=i1 *1=6000
4000=i2 * 1= 4000
i1/i2=6000/4000=3/2
=3:2
40. If ratio of profit of A and B is 4:5 and they together invested Rs.90,000 then money invested by B is
Solution:
profit of A and B is 4:5 respectively
4x+5x=90000
9x=90000
x=10000
so,money invested by B is 5x=5*10000=50000
41. In a company there are 5 partners A,B,C,D,E. They invested money in the ratio of 1:2:3:4:5. If after one year if there is a profit of Rs.15,000. Then share of E will be ?
Solution:
5 partners A,B,C,D,E are invested money in the ratio of 1:2:3:4:5
Total profit = 15000
share of E = Profit*ratio(E)/(ratio(A)+ratio(B)+ratio(C)+ratio(D)+ratio(E))
= 15000*5/(1+2+3+4+5)=5000
so answer will be 5000
42. A and B enter into a partnership and invest Rs. 12,000 and Rs. 16,000 respectively. After 8 months, C also joins the business with a capital of Rs. 15,000. The share of C in a profit of Rs. 45,600 after two years is
Solution:
For 2yrs means 24 mnths
A=(24*12)=288
B=(24*16)=384
C=(16*15)=240
Profit=45,600
Share of C is=(240/912)*45600
=12000
43. Anil and Ravi invest Rs.60,000 and Rs.40,000 and they got loss of Rs.5,000 at the end of year. Then what was the loss for Ravi in Percentage?
Solution:
ratio of their investment is 3:2
so the lost of ravi is 2000rs
40000*(x/100)=2000
then x=5%
Solution:
Ration is 4:8:5 .
Total amount in 1 Rupee coin is = Rs. 4x*1
Total amount in 2 Rupee coin is = Rs. 8x*2
Total amount in 5 Rupee coin is = Rs. 5x*5
So, 4x+16x+25x = 90; x=2
So no. of 5 rupee coin is = 5x = 10.
(or)
4x*1+8x*2+5x*5=90(coz given ratio is 4:8:5)
45x=90
x=2
So no. of 5 rupee coin is = 5x = 10
2. More than half of the members of a club are ladies.If 4/7 of the ladies and 7/11 of the gents in the club attended the meeting,then what is the smallest number that club could have?
Solution:
it would be 25 in smallest form , as for every 7 women 4 attended the meeting so for this ratio we can assume women to be (2*4/2*7) = (8/14) like there are 8 women attended the meeting from 14 women ,and for every 11 men 7 attended the meeting ,
so overall ( as per condition women are more than half of total members so we can say there are 11 men and 14 women ,as 14 women > 11 men )
i.e 11 men + 14 women gives 25 members for the club.
3. Three person Anil, Ram and Rishi whose salary together amounts to Rs. 81,000 spends 80%, 85% and 75% of their salaries respectively. If their savings are in the ratio of 8 : 9 : 20, find the salary of Ram.
Solution:
1/5x = 8 ---> x = 40
3/20y = 9 ---> y = 60
1/4z = 20 ---> z= 80
Ratio of their salary's = 40 : 60 : 80 = 2 : 3 : 4
Ram's salary = 3/9 × 81000 = 27000
4. steward assign 1/8th of his monthly salary for food.stewards total food bill for the month is rs.6500.what is stewards yearly salary?
Solution:
let steward monthly sal=x
1/8*x=6500=>x=6500*8=52000(total 1 month sal),
but given there his yearly sal=12*52000=624000
(or)
stewards total one month salary is
8*6500 = 52000
so his one year salary is 52000*12
which is 624000
5. The least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ratio less than 16 : 21, is?
Solution:
(6 - x) / (7 - x) < 16/21
=> 21 (6 - x) < 16 (7 - x)
=> 5x > 14
=> x > 2.8
So, Answer is 3.
6. A Product is supported each week by the same three customer service Representatives (CSR's). Last month the first CSR took 450 calls, the second took 350 calls, and the third took 300 calls. This month the job will consists of 1500 calls. If the three CSR's each increase their work proportionately, how many more calls will the first CSR take this month than last month?
Solution:
Last month ratio C1 : C2 : C3 = 45 : 35 : 30 => 9 : 7 : 6
This month total calls = 1500
9x + 7x + 6x = 1500
x= 1500/22 = 750/11
C1 ratio = 9 * 750/11 = 613.6 => 614 approximately
C2 ratio = 7 * 750/11 = 477.2
C3 ratio = 6 * 750/11 = 409
Calls first CSR ll take more than last month = 614 - 450 = 164
7. A started a business investing Rs 10,000. B joined him after six months with an amount of Rs 8,000 and C joined them with Rs 12,000 after another six months. The amount of profit earned should be distributed in what ratio among A, B and C respectively, four years after A started the business?
Solution:
A started the bussiness with investment 10000 for 4 years ie 48 months
B joined A after 6 months with investnemt 8000 for 3 years and 6 months i.e 42 months
c joined them after another six months i.e 1 year with an investment 12000for 3 years i.e for 36 months
By taking the ratio of 3 of the m we get
10000*48:8000*42:12000*36
=10:7:9
the profit is distributed in the ratio 10:7:9
8. Three partners Rahul, Nayan and Pooja together started a business. Twice the investment of Rahul is equal to thrice the capital of Nayan and the capital of Nayan is four times the capital of Pooja. Find the share of Nayan out of a profit Rs. 22275.
Solution:
let R , N,P be an investment of Rahul Nayan and pooja respectively
Therefore , 2R=3N ( given twice the investment of Rahul is equal to thrice the capital of Nayan) and
N=4P , now ratio of investment of N:R:P = 3N/2 : N :N/4
which is 6:4:1
therefore share of Mayan out of the profit of Rs 22275 = 4/11*22275 = 8100
9. Ramesh, xyz and Rajeev put a partnership. profit is 36000, if Ramesh and xyz ratio is 5 : 4 and xyz and Rajeev 8:9. Find Rajeev's share.
Solution:
ramesh:xyz=5:4
xyz:rajeev=8:9
ramesh:xyz:rajeev=10:8:9
rajeev=(36000*9)/27=12000
10. If 7:13::301:x then the value of ‘x’ is:
Solution:
Given the question;
7:13::301:x
7/13 = 301/x
7x = 301*13
x = 301*13/7
x = 559
11. a man buys a spirit at rs60/litre,adds water to it and then sells it at RS75/litre.what is the ratio of spirit to water if his profit in the deal is 75%
Solution:
c.p of spirit is 60/lit
s.p of 1 lit of mixture is 75
gain 75%
c.p of 1 lit of mixtre=(100/175)*75=300/7
by rule of aligation (60-300/7)/(300/7)=5:2
12. Rs 50000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 7000 Find money given by 10%?
Solution:
let x was given to a with 10% interest.
then b got 50,000 - x
interest = p*t*r /100
so
7000 =((50000 - x)*1*20)/100 +(x*1*10)/100
700000 = 1000000 - 10x
x = 30000
13. A rail network consist of 68 routes touching station A, B, C. 5 routes touches each of the three station. 2 routes touches B, C; 3 route touches B, A. 4 Route touches A, C. The ratio of route touching the A:B:C are 11:15:8. Find out how many route touches A, B, C, only. Find out also how many route touches A, B, C station?
Solution:
Given ratio as A : B : C = 11:15:8
Total routes for A = 68(11/34)= 22
A only = 22-3-5-4=10
Similarly total routes for B= 68(15/34)=30
B only = 30-3-5-2=10
Total routes for C= 68(8/34)= 16
C only = 16-4-5-2= 5
Number of routes touches A B C Only = 10+20+5=35
All routes of A B C Is= 22+30+16= 68
14. A milk seller buys milk at Rs 10 per litre and sells it at the same rate and makes a profit of 10% by adding water to it. How much water does he add to a litre of milk?
Solution:
100 ml
just do it by alligation and mixure....... cost price is (100/110)*10=>100/11.
now 0 10
100/11
10-100/11 : 100/11
ratio will be 1:10
15. The ratio of white balls and black balls is 1:2. If 9 gray balls is added it becomes 2:4:3. Then what is number of black balls ?
Solution:
3x=9
=>x=3
now white balls=2*3=6
black balls=4*3=12
so ratio of white and blak balls=1:2(proved)
blk balls=12
16. Find in what ratio will the total wages of the workers of a factory be increased or decreased. If there be a reduction in the ratio 15:11, and a increment in the wages in the ratio 22:25
Solution:
reduction in wage is =15:11
increment in wage is= 22:25
total wages ratio = reduction workers ratio* increment wage ratio
=(15/11)*(22/25)=6/5
total wages ratio =6/5
17. If the ratio of prod of 3 diff comp’s A B & C is 4:7:5 and of overall prod last yr was 4lac tones and if each comp had an increase of 20% in prod level this yr what is the prod of Comp B this yr?
Solution:
If the ratio of prod of 3 diff comp’s A B & C is 4:7:5 and of overall prod last yr was 4lac tones , then
prod of B last year = 4*7/16 = 7/4 lac tonnes
prod of B this year = 1.2*7/4 = 2.1 lac tonnes
18. Anirudh, Harish and Sahil invested a total of Rs.1,35,000 in the ratio 5:6:4 Anirudh invested has capital for 8 months. Harish invested for 6 months and Sahil invested for 4 months. If they earn a profit of Rs.75,900,then what is the share of Sahil in the profit?
Solution:
Total units={(5*8)+(6*6)+(4*4)}
=92.
sahil profit={16/92}75,900.
=13,200.
(or)
given ratio=5:6:4
Anirudh invest for 8 months,haris 4 6months and sahil for 4 months
so ratio =5*8 : 6*6 : 4*4
=40:36:16
=10:9:4
sahil's profit=(4/23)*75900
=13200
19. In what proportional should milk and water be mixed to reduce the cost of litre of milk from Rs 18 to Rs 16?
Solution:
Let total milk be x
now,
x milk costs Rs 18
so Rs 16 will have 8x/9 l milk
(unitary method)
means remaining part is water
so x-8x/9=x/9
now ratio is 8:1
20. Rs 5000 was divided among 5 men, 6 women and 5 boys, such that the ratio of the shares of men, women and boys is 5:3:2 what is the share of the boy?
Solution:
Given that ratio is 5:3:2.
Now the share of all boys will be (2/10)*5000=1000
So share of each boy will be: 1000/5=200
(or)
5x+3x+2x = 5000
x = 500
then
5 boys share = 2*500
then share of each boy = 2*500/5 = > 200
21. The sides of the triangle are in the ratio 1/2:1/3:1/5 and Its perimeter is 155 cm, what is the difference between the largest sides?
Solution:
Ratio of sides 1/2 : 1/3 : 1/5 =15 : 10 : 6
Given perimeter=155 cm , so if sides are 15x, 10x & 6x, then 15x+10x+6x =155 ,x=5
So side are 15*5=75 ,10*5=50 & 6*5=30 cm and
Difference between largest & smallest side=75 -30=45 cm
22. Kamal started a business investing Rs 9000. After five months, Sameer joined with a capital of Rs 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit ?
Solution:
Ratio of their investment => 9000 : 8000 => 9:8
Kamal's share's calculated for 12 months nd sameer's share calculated for (12-5) months...
Kamal : sameer => 9*12 : 8*7 => 108:56 => 27:14
Kamal's share = 6970*27/(27+14) = 4590
Sameer's share = 6970*14/41 = 2380
(or)
Kamal invested for 12 months and Sameer invested for 7 months.
So
Kamal:Sameer = (9000*12):(8000*7)
= 108:56
= 27:14
Sameer Ratio in profit will be
= (6970*14/41)
= Rs 2380
23. 2 vessels filled with pire contents.v1 contains 20Liter of milk v 2 contains 20 liter of water. 5 liter of milk is taken from v1 and rplaced in v2. then 4 liter of mixture is transferred from v2 to v1. find the ratio of water in v1 amount of milk in v2
Solution:
vessel m w
v1 20 0
v2 0 20
after first transfer
v1 15 0
v2 5 20
ratio of milk to water in v2 is 1:4
for 4 ltrs mixture 4/5 ltrs is milk,16/5ltrs is water
on next trnsfer
v1 15+4/5 16/5
v2 5-4/5 20-16/5
now ratio of water in v1 to milk in v2 is
(16/5)/(5-4/5)=16/21
24. There r three coins of Re 1, 50 ps, 25 ps having ratio of 13:11:3. the total sum of money is 77, then find out hw mny re. 1 coins is there?
Solution:
There r three coins of Re 1, 50 ps, 25 ps having ratio of 13:11:3.
if There r three coins of Re 1, 50 ps, 25 ps . No of coins are 13x,11x and 3x respectively..
Then
13x + 11x/2 + 3x/4 =77
x = 77*8/ (104+44+6)
= 77*8/154 = 4.
so no of 1 rupee coins
= 13x = 13*4= 52 coins.
25. A person has with him a certain number of weighing stones of 100gm, 500gm and 1 kg in the ratio of 3:5:1. If a maximum of 5 kg can be measured using weighing stones of 500gm alone, then what is the number of 100 gm stones he has?
Solution:
Number of 500gm stones
= 5kg/500gm = 10
Ratio = 3:5:1 or 6:10:2
Thus no. of 100gm stones
= 6
26. An alloy of zinc and copper contains the metals in the ratio 5 : 3. The quantity of zinc to be added to 16 kg of the alloy so that the ratio of the metal may be 3 : 1 is:
Solution:
5/8*16=10
3/8*16=6
(10+x)/6=3/1
=8 kg
27. Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
Solution:
let 100% seats are there in all then mathematics increased by 40% then
5*140/100=7
physics is increased by 50% then
7*150/100=21/2
biology increased by 75% then
8*175/100=14
then ratios of increasing seats are 7:21/2:14
14:21:28
2:3:4 is ans
28. A gets Rs.33 when a sum of money was distributed among A, B and C in the ratio 3:2:5 What will be the sum of money?
Solution:
total units=3+2+5=10
A's amount=33
let total = x
so according to d prb
(3/10) * x= 33
x=(33*10)/3
x=110
29. A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio of milk and water in the resultant mixture?
Solution:
Initially ixture has milk and water in ratio of 12:8.
when 10 ltr of mixture is removed , left mixture has milk and water in qnty/ratio of 6:4.
when 10 ltr milk is added , ratio becomes, 16:4, ratio is now 4:1
now milk is 8 lt and water is 2 lt in 10 lt mixture
again replaced by 10 lt of milk hence milk and water is in 18:2 in 20 lt mix
so ratio becomes 9:1
30. The proportion of milk and water in 3 samples is 2:1, 3:2 and 5:3. A mixture comprising of equal quantities of all 3 samples is made. The proportion of milk and water in the mixture is
Solution:
Proportion of milk in 3 samples is 2/3, 3/5, 5/8.
Proportion of water in 3 samples is 1/3, 2/5, 3/8.
Since equal quantities are taken,
Total proportion of milk is 2/3 + 3/5 + 5/8 = 227/120
Total proportion of water is 1/3 + 2/5 + 3/8 = 133/120
Proportion of milk and water in the solution is 227:133
31. An alloy of zinc and copper contains the metals in the ratio 5 : 3. The quantity of zinc to be added to 6 kg of the alloy so that the ratio of the metal may be 3 : 1 is:
Solution:
in 6kg of alloy 15/4-zinc and 9/4-copper .
so,
let extra zinc added be x
(15/4+x)/(9/4)=3/1
x=3
32. It has 20L mixutre conatins milk and water in the ratio 3:5,replace 4 litres of mixture with 4 litres of water what is the final ratio of milk and water.
Solution:
Full mixture has 7.5L milk 12.5L water if we fetch 4L mixture according to ratio it will be 1.5L milk & 2.5L water,replace this mixture from the water then it will be 6L milk and 14L water then ratio will be
6/14=3:7
(or)
Quantity of water in 16L of mix=16*(5/8)=10L
Quantity of water in 20L of new mix=(10+4)L
Quantity of milk in new mix=20-14=6L
then ratio=6/14=3:7
33. 729 ml of a mixture contains milk and water in ratio 7:2. How much of the water is to be added to get a new mixture containing half milk and half water?
Solution:
milk=(7/9)*729=567
water=(2/9)*729=162
according to question let z ml of water is added of mixture so
(729+z)*(50/100)=162+z
on solving
z=405 ml
34. In a theatre the ratio of car & two wheeler is 1:8. Total Number of tyres are 100. Find how many are cars and how many are two wheelers?
Solution:
let the no of cars be 1x and no of two wheelers be 8x
(1x*4)+(8x*2)=100
20x=100 ...x=5
1x=no of cars=5
8x=no of two wheelers=40
35. Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?
Solution:
simran=50k*3=150k
nanda=80k*2.5=200k
ratio=150k/200k=3:4
simran=3/7*24500=10500
36. A 20 litre solution conatins oil and kerosene in the ratio 3:5,replace 4 litres of mixture with 4 litres of kerosene what will be the ratio of oil and kerosene?
Solution:
When 4 liters are taken out of 20ml, amount of oil in remaining
16 lt = 3/8 * 16 = 6
Hence the remaining 10 litres would be kerosene
Now additional 4 litres of kerosene is added to the solution
So total quantity of kerosene = 14 litres
Ratio of oil:kerosene
= 6/14
= 3/7
37. It has 20 mixutre conatins mil and water in the ratio 3:5,replace 4 litres of mixture with 4 litres of water what is the final ratio of milk and water.
Solution:
the total mixture quantity=20 litre.
so,milk = 20*(3/8)=7.5
water = 12.5 (20-7.5)
when 4 litre removed,water and milk will become less in same ratio
milk = 7.5 - (4*3/8) = 6 litre
water = 12.5 - (4*5/8) = 10 litre
when 4 litre water added ,
water amount = 10+4 = 14.
ratio = 6/14 = 3/7
38. A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:
Solution:
Given that B has missed 27 times, means he attempted 54 shots..
but A fires 5 shots to B's 3
so A fires 90 shots to B's 54.
but A kills only once in 3 shots...
so
A has killed 30 Birds
(or)
Let the total no. of shots = x
shots fired by A = 5x/8;
shots fired by B= 3x/8;
killed by A= 1/3 of 5x/8= 5x/24;
missed by B= 1/2 of 3x/8= 3x/16;
A.T.Q :- 3x/16=27;
or x= 144;
so A has kiled= 5x/24= (5*144)/24= 30.
39. If A and B get profits of Rs. 6000 and Rs. 4000 respectively at the end of year the ratio of their investments are
Solution:
profit=Investment * Time
so,
6000=i1 *1=6000
4000=i2 * 1= 4000
i1/i2=6000/4000=3/2
=3:2
40. If ratio of profit of A and B is 4:5 and they together invested Rs.90,000 then money invested by B is
Solution:
profit of A and B is 4:5 respectively
4x+5x=90000
9x=90000
x=10000
so,money invested by B is 5x=5*10000=50000
41. In a company there are 5 partners A,B,C,D,E. They invested money in the ratio of 1:2:3:4:5. If after one year if there is a profit of Rs.15,000. Then share of E will be ?
Solution:
5 partners A,B,C,D,E are invested money in the ratio of 1:2:3:4:5
Total profit = 15000
share of E = Profit*ratio(E)/(ratio(A)+ratio(B)+ratio(C)+ratio(D)+ratio(E))
= 15000*5/(1+2+3+4+5)=5000
so answer will be 5000
42. A and B enter into a partnership and invest Rs. 12,000 and Rs. 16,000 respectively. After 8 months, C also joins the business with a capital of Rs. 15,000. The share of C in a profit of Rs. 45,600 after two years is
Solution:
For 2yrs means 24 mnths
A=(24*12)=288
B=(24*16)=384
C=(16*15)=240
Profit=45,600
Share of C is=(240/912)*45600
=12000
43. Anil and Ravi invest Rs.60,000 and Rs.40,000 and they got loss of Rs.5,000 at the end of year. Then what was the loss for Ravi in Percentage?
Solution:
ratio of their investment is 3:2
so the lost of ravi is 2000rs
40000*(x/100)=2000
then x=5%
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