# Ratio and Proportion: Practice Set - 1

1. A bag contains 50 paise, 25 paise and 10 paise coins in the ratio 5 : 9 : 4, amounting to Rs 206. Find the number of 25 paise coins.
a) 200
b) 360
c) 160
d) 300
e) 240
2. There is certain numbers of toys in the box. They are divided into such a way that the person who gets 1/4 of the whole gets thrice of what the others get on an average. Find the number of people amongst whom the toys are distributed?
a) 8
b) 9
c) 10
d) 11
e) 12
3. A mixture contains alcohol and water in the ratio 4:3. If 5 liters of water is added to the mixture, the ratio becomes 4:5. Find the quantity of alcohol in the given mixture.
a) 8 litres
b) 10 litres
c) 12 litres
d) 15 litres
e) 22 litres
4. The salaries of A, B, and C are in the ratio of 1 : 2 : 3. The salary of B and C together is Rs. 6000. By what percent is the salary of C more than that of A?
a) 100%
b) 200%
c) 300%
d) 500%
e) 600%
5. A sum of Rs.312 was divided among 100 boys and girls in such a way that the boy gets Rs.3.60 and each girl Rs. 2.40 the number of girls is
a) 30
b) 35
c) 40
d) 45
e) 50
6. 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 ?
a) 1 : 2 : 3
b) 2 : 3 : 4
c) 3 : 4 : 5
d) 4 : 5 : 6
e) 3 : 5 : 7
7. The ratio of incomes of A and B is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs 1600, then what is the income of A ?
a) Rs.2500
b) Rs.3500
c) Rs.4000
d) Rs.4500
e) Rs.5000
8. A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is :
a) 2 : 3
b) 4 : 7
c) 5 : 6
d) 9 : 5
e) 5 : 9
9. If the ratio of the ages of two friends A and B is in the ratio 3 : 5 and that of B and C is 3 : 5 and the sum of their ages is 147, then how old is B?
a) 27
b) 45
c) 49
d) 76
e) 73
10. A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long?
a) 12
b) 36
c) 48
d) 60
e) 72
Solutions:
1. B) Let the number of coins of 50p , 25p and 10p be 5x, 9x and 4x
Therefore,  (5x/2) + (9x/4) + (4x/10) = 206 => x = 40
Hence, No of 50 p coins = 5x = 5 * 40 = 200; 25 p coins = 9x = 9*40= 360 and 10 p coins = 4x = 4*40=160
2. C) If the person who gets 1/4 of the whole gets thrice of what the others get on an average,
each one will get =1/3×1/4=1/12 of the whole.
Therefore, if there are k persons other than the person who gets one-fourth, then
1/4 + k/12 = 1 k=9
Hence, total number of people = 10.
3. B) Let the quantity of alcohol and water be 4x litres and 3x litres respectively. Then,
4x/(3x + 5) = 4/5 => 20x = 12x + 20 => 8x = 20 => x = 5/2 = 2.5
Quantity of alcohol = (4 * 2.5) litres = 10 litres.
4. B) Let the salaries of A, B, C be x, 2x and 3x respectively.
Then,2x + 3x = 6000  => x = 1200.
A's salary = Rs. 1200, B's salary = Rs. 2400, and Cs salary Rs. 3600.
Excess of C's salary over A's=[ (2400 /1200) x 100] = 200%.
5. C) Step (i): Let x be the number of boys and y be the number of girls.
Given total number of boys and girls = 100
x+y=100 -------------- (i)
Step (ii): A boy gets Rs. 3.60 and a girl gets Rs. 2.40
The amount given to 100 boys and girls = Rs. 312
3.60x + 2.40y = 312 -------------- (ii)
Step (iii):
Solving (i) and (ii)
3.60x + 3.60y = 360 --------- Multiply (i) by 3.60
3.60x + 2.40y = 312 --------- (ii)
1.20y = 48
y = 48 / 1.20 = 40
=> Number of girls = 40
6. B) Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
[(140/100) × 5x],[(150/100) × 7x] and [(175/100) × 8x]
7x, 21x/2 and 14x.
The required ratio =7x : 21x/2 : 14x
14x : 21x : 28x
2 : 3 : 4
7. C) Suppose the income of A and B is 5x and 4x respectively and their expenditures is 3y and 2y respectively.
Therefore , 5x – 3y = 1600 and 4x – 2y = 1600 , On solving both the equations ,
x  = 800 , y = 800
Thus income of A = 5x = 5*800 = Rs 4000
8. D) Dog : Hare = (3*3) leaps of hare : 5 leaps of hare = 9 : 5.
9. B) The ratio of the ages of A and B is 3 : 5.
The ratio of the ages of B and C is 3 : 5.
B's age is the common link to both these ratio. Therefore, if we make the numerical value of the ratio of B's age in both the ratios same, then we can compare the ages of all 3 in a single ratio.
The can be done by getting the value of B in both ratios to be the LCM of 3 and 5 i.e., 15.
The first ratio between A and B will therefore be 9 : 15 and
the second ratio between B and C will be 15 : 25.
Now combining the two ratios, we get A : B : C = 9 : 15 : 25.
Let their ages be 9x, 15x and 25x.
Then, the sum of their ages will be 9x + 15x + 25x = 49x
The question states that the sum of their ages is 147.
i.e., 49x = 147 or x = 3.
Therefore, B's age = 15x = 15*3 = 45
10. C) If you double the sides of a cube, the ratio of the surface areas of the old and new cubes will be 1: 4. The ratio of the volumes of the old and new cubes will be 1: 8.
Weight is proportional to volume. So, If the first weighs 6 pounds, the second weighs 6x8 pounds =48.

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