Question

A and B together can do a piece of work in 12 days which B and C together do in 16 days. After A has been working at it for 5 days, B for 7 days, C finished it in 13 days. In how much time C alone will do the work?

Answer 1

Hint:First we find the one day work for A, B and C.Here a given that the work doing by A and B together and also B and C together so we can split the work of A’s, B’s and C’s Finally, we will find time taken by C to complete the work.

Complete step-by-step answer:
Here, it is given that,
A and B together can do a piece of work in 12 days and B and C together do in 16 days
A works for 5 days, B works for 7 days than C completes the remaining work in 13 days
Let’s solve this question arithmetically:
As A and B can finish the work in 12 days’ time, hence
(A + B)’s one day’s work = $${\displaystyle \frac{1}{12}}$$
Similarly
(B + C)’s one day’s work = $${\displaystyle \frac{1}{16}}$$
Now, A’s 5 days’ work + B’s 7 days’ work + C’s 13 days’ work = 1
A’s 5 days’ work + B’s 5 days’ work + B’s 2 days’ work + C’s 2 days’ work + C’s 11 days’ work = 1
Or {(A + B)’s 5 days’ work} + {(B + C)’s 2 days’ work} + C’s 11 days’ work = 1
i.e. ${\displaystyle \frac{5}{12}}+{\displaystyle \frac{2}{16}}$ + C’s 11 days’ work = 1
or C’s 11 days’ work $$=1-\left({\displaystyle \frac{5}{12}}+{\displaystyle \frac{2}{16}}\right)$$
or C’s 11 days’ work $$=1-{\displaystyle \frac{13}{24}}$$
or C’s 11 days’ work $$={\displaystyle \frac{11}{24}}$$
or C’s 1 day’s work $$={\displaystyle \frac{11}{24}}\times {\displaystyle \frac{1}{11}}={\displaystyle \frac{1}{24}}$$
Therefore, C alone can finish the complete work in 24 days.

Note:Mathematically we say that if A can complete a work in n days, work done by A in $$1$$ day is $${\displaystyle \frac{1}{n}}$$. And if A can complete $${\displaystyle \frac{1}{n}}$$ part of the work in $$1$$ day, then A will complete the work in n days.