# Ratio and Proportions – Part 01

(01) In a mixture of 60 liters, the ratio of milk and water is 2:3. How much water must be added to this mixture so that the ratio of milk and water becomes 1:2 ?

Sol:
Given ratio- 2:3

Quantity of milk in the mixture = 2/5 × 60 = 2 × 12 = 24 liters
Also, quantity of water in the mixture = 3/5 × 60 = 36 liters

Let the quantity of water added be x liters.

As per question-

x + 36 = 48

x = 48 – 36 = 12 liters

Thus, the additional quantity of water which needs to be added to the mixture is 12 liters

(02) If three numbers are in the ratio of 1: 3: 5 and half the sum is 9, then the ratio of the cubes of the numbers is:

Let the first number be x, second number be 3x and 5x.

As per question-
x + 3x + 5x / 2 = 9
9x = 18
x = 18/9 = 2

Thus,
first number = 2,
second number = 3 × 2 = 6
and third number = 5 × 2 = 10

Cube of first number = (2)³ = 8
Cube of second number = (6)³ = 216
Cube of third number = (10)³ = 1000

Therefore, required ratio = 8 : 216 : 1000 = 1 : 27 : 125

(03) The ratio between two numbers is 7 : 11 and their LCM is 154. The first number is

Let the first number be 7x and the second number be 11x.

As per question-
LCM of these two numbers = 154

(7 × 11) x = 154

77x = 154

x = 154/77

x = 2

Thus, the first number = 7x = 7 × 2 = 14

(04) The incomes of P and Q are in the ratio 1:2 and their expenditures are in the ratio 1:3. If each saves Rs. 500, then P’s income can be:

Let the income of P be x and that of Q be 2x
Also, let the expenditure of P be y and that of Q be 3y

As per question-

x – y = 500 ………………….. (i)

2x – 3y = 500 ……………….. (ii)

Multiplying eq (i) by 2 and eq (ii) by 1 and then subtracting-

y = 500

Therefore, x = 500 + y = 500 + 500 = 1000
Thus, income of P is Rs. 1000

(05) Divide Rs. 1360 among p, q and r such that p gets 2/3rd  of what q gets and q gets 1/4th of what r gets. Now, the share of r is

Let the share of r be Rs. x
Then, the share of q will be Rs. x/4
Also, the share of p = 2/3 of x/4 = Rs. x/6

According to the question-
=> x + x/4 + x/6 = 1360 => 17x = 12 × 1360
=> x = 960

Thus, the share of r is Rs. 960