In this page ratio and proportion solution16 we are going to see solution of each question from the worksheet ratio and proportion.

(35) In the regiment, the ratio of the number of officers to the number of soldiers was 3 : 31 before the battle. In the battle 6 officers and 22 soldiers were killed. The ratio between the number of officers to the number of soldiers now is 1 : 13. Find the number of officers and soldiers before the battle.

**Solution: **

The ratio of the number of officers to the number of soldiers was 3 : 31

Number of officers = 3 x

Number of soldiers = 31 x

Number of officers killed in the battle = 6

Number of soldiers killed in the battle = 22

(3 x – 6) : (31 x – 22) = 1 : 13

(3 x - 6)/(31 x – 22) = 1/13

13 (3 x – 6) = 1 (31 x – 22)

39 x – 78 = 31 x – 22

39 x – 31 x = - 22 + 78

8 x = 56

x = 56/8

x = 7

Number of officers before the battle = 3 (7) = 21

Number of soldiers before the battle = 31 (7) = 217

(36) The cost of production of the radio set is Rs.1800, divided between the materials, labour and overheads, in the ratio 4 : 3 : 2. Calculate the cost of material used in the radio set.

**Solution:**

Cost of production of the radio set = Rs. 1800

4 x + 3 x + 2 x = 1800

9 x = 1800

x = 1800/9

x = 200

Cost of materials = 4 (200) = Rs.800

Cost of labour = 3 (200) = Rs.600

Cost of overheads = 2 (200) = Rs.400

Cost of materials, labour and overheads are Rs.800 , Rs.600 and Rs.400

ratio and proportion solution16 ratio and proportion solution16

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