Question

$A$ can do a certain work in the same time in which $B$ and $C$ together can do it. If $A$ and $B$ together could do it in $10$ days and $C$ alone in $50$ days, then $B$ alone could do it in

• A. $15$ days
• B. $20$ days
• C. $25$ days
• D. $30$ days

Answer 1

The correct option is C $25$ days

(A+B)'s 1 day's work$=\frac{1}{10}$

C's 1 day's work$=\frac{1}{50}$

(A+B+C)'s 1 day's work$=\frac{1}{10}+\frac{1}{50}=\frac{6}{50}=\frac{3}{25}.....\left(I\right)$

According to the question

A's 1 day's work=(B+C) 1day's work.........(II)

From I and II we get

$2\times$(A's one day's work)$=\frac{3}{25}$

A's one day's work$=\frac{3}{50}$

$\therefore$ B's 1 day's work$=\frac{1}{10}-\frac{3}{50}=\frac{2}{50}=\frac{1}{25}$

Hence B alone could do the work in 25 days.