# In a television game show, the prize money of ₹ 1,00,000 is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners?

**Solution:**

Let the number of winners be x and the prize amount be y.

If winners increases then, the prize amount will decrease. Hence, they are inversely proportional.

Two numbers x and y are said to be in inverse proportion when an increase in one quantity decreases the other quantity and vice versa.

xy = k or x = (1/y) k

where k is a constant.

x₁y₁ = x₃y₃

1 × 100000 = 4 × y₃

y₃ = 1 × 100000/4

y₃ = 25000

1 × 100000 = 5 × y₄

y₄ = 1 × 100000/5

y₄ = 20000

1 × 100000 = 8 × y₅

y₅ = 1 × 100000/8

y₅ = 12,500

1 × 100000 = 10 × y₆

y₆ = 1 × 100000/10

y₆ = 10000

1 × 100000 = 20 × y₇

y₇ = 1 × 100000/20

y₇ = 5000

Thus, the complete table is shown below:

Number of winners |
1 | 2 | 4 | 5 | 8 | 10 | 20 |

Prize for winners |
1,00,000 | 50,000 | 25,000 | 20,000 | 12,500 | 10,000 | 5,000 |

**Video Solution:**

## In a television game show, the prize money of ₹ 1,00,000 is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners?

### Maths NCERT Solutions Class 8 - Chapter 13 Exercise 13.2 Question 2

**Summary:**

In a television game show, the prize money of ₹ 1,00,000 is to be divided equally amongst the winners. The table is completed and the prize money given to an individual winner is inversely proportional to the number of winners since, if winners increases then, the prize amount will decrease.