Shikha works in a factory. In one week she earned ₹ 3,900 for working 47 hours, of which 7 hours were overtime. The next week she earned ₹ 4,160 for working 50 hours, of which 8 hours were overtime. What is Shikha's hourly earning rate?

Let's assume earning's of Shikha be ₹ x per hour for regular hour and ₹ y per hour for overtime.

Given,

In one week she earned ₹ 3,900 for working 47 hours, of which 7 hours were overtime.

Shikha works for 40 hours regular and 7 hours overtime.

40x + 7y = 3900 ………………..(1)

Given,

The next week she earned ₹ 4,160 for working 50 hours, of which 8 hours were overtime.

Thus, she works for 42 hours regular and 8 hours overtime.

42x + 8y = 4160 ………………..(2)

Multiplying equation (1) by 8 , we get :

⇒ 8(40x + 7y) = 3900 x 8

⇒ 320x + 56y = 31200 ………………..(3)

Multiplying equation (2) by 7, we get :

⇒ 7(42x + 8y) = 4160 x 7

⇒ 294x + 56y = 29120 ………………..(4)

Subtracting equation (4) from (3) we get,

⇒ 320x + 56y - (294x + 56y) = 31200 - 29120

⇒ 320x - 294x + 56y - 56y = 31200 - 29120

⇒ 26x = 2080

⇒ x = $\dfrac{2080}{26}$

⇒ x = 80.

Substituting the value of x in (1) we get,

⇒ 40(80) + 7y = 3900

⇒ 3200 + 7y = 3900

⇒ 7y = 700

⇒ y = $\dfrac{700}{7}$

⇒ y = 100.

Hence, Shikha's earning is ₹ 80 per regular hour and ₹ 100 per hour for over time.