Question

A and B can do a work in 12 days, B and C can do the same work in 15 days and A and C can complete the work in 20 days.Days required by A, B and C working together is (in days) ___

Answer 1

Let a, b and c be the % of the work done by A, B and C in one day respectively.

$A\&B$ can complete the work in 12 days $a+b=\frac{100}{12}\%=8.33\%...\left(i\right)$

$B\&C$ can complete the work in 15 days $b+c=\frac{100}{15}\%=6.67\%....\left(ii\right)$

$A\&C$ can complete the work in 20 days $a+c=\frac{100}{20}\%=5\%....\left(iii\right)$

Adding (i), (ii) and (iii)

$2(a+b+c)=20\%\Rightarrow (a+b+c)=10\%$

So, working together they finish $10\%$ of work in a day. So, they can complete the work in 10 days.