**(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 2/3 ^{rd} of what q gets and q gets 1/4^{th} 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**