Question

A and B work together and complete a given work in x days. If A alone completes this work in x + 2 days and B alone completes this work in x + 8 days, then the value of x is
1. 3
2. 4
3. 5
4. 2

Answer 1

Correct Answer - Option 2 : 4

Calculation:

A + B can complete the work in x days,

A alone can complete in x + 2 days

B alone can complete in x + 8 days

Work done by A in 1 day = 1/(x + 8)

Work done by B in 1 day = 1/(x + 2)

Work done by A + B in 1 days = 1/x

⇒ 1/x = 1/(x + 8) + 1/(x + 2)

⇒ 1/x = (2x + 10)/(x² + 10x + 16)

⇒ x = (x2 + 10x + 16)/(2x + 10)

⇒ 2x² + 10x = x2 + 10x + 16

⇒ x2 = 16

∴ x = + 4 or - 4

But days can not be negative, hence x = 4 days