A takes 8 hours to copy a 50-page manuscript while B can copy the same manuscript in 6 hours. How many hours would it take them to copy a similar 100-page manuscript, if they work together?

Question

Question

This question was previously asked in

Haryana CET Previous Year Paper (Held On: 6 Nov 2022 Shift 2)

Answer 1

Given :

Time taken by A = 8 Hour

Time taken by B = 6 Hour

Solution :

Taking LCM of their timing to get the total work :

⇒ 8 = 2 × 2 × 2

⇒ 6 = 2 × 3

LCM = 2 × 2 × 2 × 3 = 24

Total work = 24 Unit = 50 page

48 Unit = 100 page

Efficiency of A = 24 / 8

⇒ 3 Unit/Hour

Efficiency of B = 24 / 6

⇒ 4 Unit/Hour

According to the question time taken by both A and B working together to complete the 100 page manuscript :

⇒ 48 / 7

⇒ \(6\frac{6}{7}\) Hours

Hence the correct answer is "\(6\frac{6}{7}\) Hours".