# 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.

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 13

**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?

NCERT Solutions Class 8 Maths 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.

**☛ Related Questions:**

- Which of the following are in inverse proportion? (i) The number of workers on a job and the time to complete the job. (ii) The time taken for a journey and the distance travelled in a uniform speed. (iii) Area of cultivated land and the crop harvested.
- In a television game show, the prize money of ₹ 1,00,000 is to be divided equally amongst the winners.
- Rehman is making a wheel using spokes. He wants to fix equal spokes n such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table. (i) Are the number of spokes and the angle formed between the pairs of consecutive spokes in inverse proportion?
- If a box of sweets is divided among 24 children, they will get 5 sweets each. How many would each get, if the number of the children is reduced by 4?

visual curriculum