# A factory requires 42 machines to produce a given number of articles in 63 days. How many machines would be required to produce the same number of articles in 54 days?

**Solution:**

Let the number of machines be y and the number of days be x.

If the number of days decreases, the number of machines required will increase. So, they are inverse proportion.

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.

Hence, x₁y₁ = x₂y₂

63 × 42 = 54 × y₂

y₂_{ }= (42 × 63)/54

y₂_{ }= 49

Thus, 49 machines will be required to produce the same number of articles in 54 days.

**Video Solution:**

## A factory requires 42 machines to produce a given number of articles in 63 days. How many machines would be required to produce the same number of articles in 54 days?

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

**Summary:**

A factory requires 42 machines to produce a given number of articles in 63 days. 49 machines would be required to produce the same number of articles in 54 days.