Question

Parul and Karan are employed to complete a piece of work. Parul takes 6 days more to complete the work than when they work together and Karan takes 54 days more to complete a work, than when they work together.find the time required to finish the work together.
1. 18 days
2. 24 days
3. 16 days
4. 17 days

Answer 1

Correct Answer - Option 1 : 18 days

Given

Parul takes 6 days more and Karan takes 54 days more to complete the work, than to complete a work together.

Calculation

Let the Parul and Karan together complete a work in x days

Parul = (x + 6) days

Karan = (x + 54) days

1/(x + 6) + 1/(x + 54) = 1/x

⇒ [x + 54 + x + 6]/(x + 6) (x + 54) = 1/x

⇒ (2x + 60)/(x² + 54x + 6x + 324) = 1/x

⇒ 2x² + 60x = x² + 60x + 324

⇒ x² = 324

⇒ x = 18

∴ Parul and Karan complete the work in 18 days.