Question

P does a piece of work alone in 3 days.
P and Q together do the work in 2 days.
How many days will Q take to do the
work alone?​
plz explain

Answer 1

Given:-

P can do a piece of work alone in 3 days

and, P & Q can both do the work in 2 days.

Required answer:-

Time in which Q can finish the work alone.

Solution:-

Let Q can do a piece of work alone in x days.

$\sf \footnotesize{ \therefore{Q's \: 1 \: day \: work = \frac{1}{x} }}$

P can do piece of work alone in = 3 days

$\sf \footnotesize{ \therefore{P's \: one \: day \: work = \frac{1}{3} }}$

$\sf \footnotesize{ \therefore{P \: and \: Q's \: one \: day \: work = \frac{1}{3} + \frac{1}{x} = \frac{x + 3}{3x} }}$

$\sf \footnotesize \implies{P \: and \: Q \: finish \: work \: in = \frac{3x}{x + 3}}$

But it is given that they can finish work in 2 days,

$\sf \footnotesize{ \therefore{ \frac{3x}{x + 3} = 2}}$

$\sf \footnotesize \implies{3x = 2x + 6}$

$\sf \footnotesize{ \implies{x = 6}}$

Hence, Q can finish work alone in 6 days.