Question

A's work efficiency is three times than B's and so A is able to finish a job in 60 days less than B. If they work together, they can do this job in ___ days.

[Enter your answer in decimals]

Answer 1

Time taken by A : Time taken by B = 1 : 3
That is if A takes 1 day to do the work , B will take 3 days.
Let the number of days taken by A be $x$.
Hence B will take $x+60$ days

A's work B's work

1 3

$x$ $x+60$

$\therefore 3x=x+60$
$\Rightarrow 2x=60$
$\Rightarrow x=30$
Hence, if A takes 30 days to finish the work , then B will take $x+60$ = 90 days.
A's one day of work = $\frac{1}{30}$
B's one day of work = $\frac{1}{90}$
Amount of work done by them in one day if they work together is;
$\frac{1}{30}+\frac{1}{90}=\frac{3+1}{90}=\frac{4}{90}$
Hence, together they will complete in the $\frac{90}{4}$ days, which is, 22.5 days.