A complete $$\frac{7}{{10}}$$ of a work in 15 days, then he completed the remaining work with the help of B in 4 days. In how many day A and B can complete entire work together?

A. $$10\frac{1}{2}\,\,{\text{days}}$$

B. $$12\frac{2}{3}\,\,{\text{days}}$$

C. $$13\frac{1}{3}\,\,{\text{days}}$$

D. $$8\frac{1}{4}\,\,{\text{days}}$$

Answer: Option C

Solution(By Examveda Team)

$$\frac{7}{{10}}$$ part of work has been completed by A in 15 days. Then,
Rest work = 1 - $$\frac{7}{{10}}$$ = $$\frac{3}{{10}}$$ part
Given, That $$\frac{3}{{10}}$$ part of the work is completed by A and B together in 4 days. Means,
(A + B) completed the $$\frac{3}{{10}}$$ of work in 4 days
So, (A + B)'s 1 day's work = $$\frac{3}{{10 \times 4}}$$  = $$\frac{3}{{40}}$$
Hence,
(A + B) can complete the work in $$\frac{{40}}{3}$$ = $$13\frac{1}{3}$$ days