Ratio and Proportion Questions & Answers

Question. 1.

In a mixture of 40 litres, the ratio of milk and water is 4:1. How much water must be added to this mixture so that the ratio of milk and water becomes 2:3.
(a) 20 litres
(b) 32 litres
(c) 40 litres
(d) 30 litres

Question. 2.

If three numbers are in the ratio of 1:2:3 and half the sum is 18, then the ratio of squares of the numbers is:
(a) 6: 12: 13
(b) 1: 2: 4
(c) 36: 144: 324
(d) None of these

Question. 3.

The ratio between the two numbers is 3:4 and their LCM is 180. The first number is:
(a) 60
(b) 45
(c) 15
(d) 20

Question. 4.

The incomes of A and B are in the ratio 3:2 and their expenditures are in the ratio 5:3. If each saves Rs. 1000, then, A's income is
(a) Rs. 3000
(b) Rs. 4000
(c) Rs. 6000
(d) Rs. 9000

Question. 5.

The students in three batches at Made Easy are in the ratio 2 : 3 : 5. If 20 students are increased in each batch, the ratio change to 4:5:7. The total number of students in the three batches before the increase were.
(a) 10
(b) 90
(c) 100
(d) 150

Question. 6.

The difference between the two positive numbers is 10 and the ratio between them is 5:3. Find the product the two numbers
(a) 375
(b) 175
(c) 275
(d) 125

Question. 7.

Four numbers in the ratio 1:3:4:7 add up to give a sum of 105. Find the value of the biggest number
(a) 42
(b) 35
(c) 49
(d) 63

Question. 8.

If Rs. 58 is divided among 150 children such that each girl and each boy gets 25 p and 50 p respectively. Then how many girls are there?
(a) 52
(b) 54
(c) 68
(d) 62

Solutions:

Ans 1. (c)

SolutionsLet water is x
4 x : x = milk : water
32: 8 = 4x : x (since total 40 liters)

Ans 2.(c)

Let numbers are
x : 2x : 3x also it is given that

6x = 36, x = 6
6 : 12 : 18
The ratio of squares 36: 144 : 324: or also 1 : 4 : 9

Ans 3. (b)

Let number are 3x and 4x
3x 4x =HCF ✕ 180

Clearly, HCF will be x
12x² = x 180, x = 15
Number will be 45:60
Note: if there are two number

Ans 4.(c)

Let incomes are 3x:2x
Expenditures are 5y:3y
Then
3x­­–5y = 1000            …..(i) also
2x–3y = 1000                   …..(ii)
from (i) and (ii) we get
6x-10y = 2000
+6x-9y = 3000
-y =-1000
y=1000, x= 2000
A's income is 6000

Ans 5.(c)

let students are 2x: 3r: 5x now According to the given condition
2x+20 : 3x+20 : 5x + 20 = 4 : 5 : 7
x = 10
20:30:50 = 2:3:5 and after adding 20
40:50:70

Ans 6. (a)

x-y = 10              ……(i)
x:y = 5:3            ……(ii)
x:y = 5t:3t         ……(iii)
according to (i) and (iii)
5t-3t = 10
2t = 10, t = 5
x = 25, y = 15
Product of two numbers = 375

Ans 7.(c)

x : 3x : 4x : 7x
re four numbers also
x + 3x + 4x + 7x = 105
15x = 105, x = 7, 7r = 49

Ans 8.(c)

Let the number of girls and boys are x and y then
0.25x + 0.5 = 58         ….(i)
also
x + y = 150                 ….(ii)
from (i) and (ii) we get
0.5x + y = 116
x + y = 150
So, 0.5x = 34, x = 68, y = 82