**(01) The number to be added to each of the numbers 7, 16, 43, 79 to make the numbers in the proportion**

Let the required number be x.

7 + x : 16 + x = 43 + x : 79 + x

x = 5

Hence number 5 should be added to each number to make it a proportion

**(02) If there is a reduction in the number of workers in a factory in the ratio 15 : 11 and an increment in their wage in the ratio 22 : 25, then the ratio by which the total wage of the workers should be decreased is:**

**(03) A policeman starts to chase a thief. When the thief goes 10 steps, the policeman moves 8 steps and 5 steps of the policeman are equal to 7 steps of the thief. The ratio of the speeds of the policeman and the thief is:**

Given –> 5P = 7T

P = 7/5 T

Speed of Police / Speed of Thief = 8P / 10T

= (8 × 7T/5) / 10T

= 56 / 50 = 28 / 25 = 28 : 25

**(04) There are two containers of equal capacity. The ratio of milk to water in the first container is 3 : 1 and in the second container is 5 : 2. If they are mixed up, the ratio of milk to water in the mixture will be:**

Milk in first container = ¾

Milk in second container = 5/7

Milk in new container = ¾ + 5/7 = 41/28

Water in first container = ¼

Water in second container = 2/7

Water in new container = ¼ + 2/7 = 15/28

**Required ratio** = 41/28 : 15/28 = **41 : 15**

**(05) Rs. 1740 is divided among A, B and C such that 0.5 of A = 0.6 of B = 0.75 of C. Then, C will get:**

==> 0.5 of A = 0.6 of B = 0.75 of C

==> 5/10 A = 6/10 B = 75/100 C

==> A/2 = 3B/5 = 3C/4

**10A = 12B = 15C**

A : B : C = 180 : 150 : 120 = 6x : 5x : 4x

6x + 5x + 4x = 1740

x = Rs. 116

Share of C = 4x = 4 ( 116 ) = Rs. 464

**(06) A person bought some rice and wheat for Rs. 380. The ratio of weight of rice and wheat is 4 : 3 and the price of equal amount of rice and wheat is in the ratio 5 : 6. The rice was bought of worth**

**(07) The ratio of number of balls in bags x, y is 2 : 3. Five balls are taken from bag y and are dropped in bag x, number of balls are equal in each bag now. Number of balls in each bag now is**

Balls in bag x = 2x and Balls in bag y = 3x

3x – 5 = 2x + 5

3x – 2x = 5 + 5

x = 10

**Balls in bag x** = 2 (10) + 5 = **25 **

and **Balls in bag y** = 3 (10) – 5 = **25**

(08) **A man ordered 4 pairs of black socks and some pairs of brown socks. The price of a pair of black socks is double that of a brown pair. While preparing the bill, the clerk interchanged the number of black and brown pairs by mistake which increased the bill by 50%. The ratio of the number of black and brown pairs of socks in the original order was**:

New bill = 2x + 4

3 ( 8 + x ) = 2 ( 2x + 4 )

x = 16

Brown pairs = 16, Black pairs = 4,

**Required ratio** = 4 : 16 =** 1 : 4**