Question

Two workers P and Q working together completed a job in 10 days. If P worked four times as efficiently as he actually did and Q worked ${\frac{2}{3}}^{rd}$ as efficiently as he actually did, the work would have been completed in 3 days. P alone could complete the work in:

• A. 12.5 days
• B. 7.5 days
• C. 6.25 days
• D. 15 days

Answer 1

The correct option is A

12.5 days

Let P’s 1 day’s work = ‘x’ and Q’s 1 day’s work = ‘y’

Then, $x+y=\frac{1}{10}$ and $4x+\frac{2}{3}y=\frac{1}{3}$

Solving, we get - x = $\frac{2}{25}$ and y = $\frac{1}{50}$

∴ P’s 1 day’s work = $\frac{2}{25}$

So, P alone could complete the work in $\frac{25}{2}=12\frac{1}{2}$ days