Question

A can do a piece of work in 30 days, B in 50 days and C in 40 days. If A is assisted by B on one day and by C on the next day alternately work will be completed in

• A. $17\frac{32}{35}days$
• B. $19\frac{2}{3}days$
• C. $16\frac{31}{37}days$
• D. $18\frac{1}{3}days$

Answer 1

The correct option is A $17\frac{32}{35}days$

(A + B)'s 1 day's work
$=\frac{1}{30}+\frac{1}{50}=\frac{8}{150}$

$\therefore$ (A+C)'s 1day's work

$=\frac{1}{30}+\frac{1}{40}=\frac{7}{120}$

$\therefore$ Work done in first 2 days

$=\frac{8}{150}+\frac{7}{120}=\frac{67}{600}$

Work done in 8 × 2 = 16 days

$=\frac{67\times 8}{600}=\frac{67}{75}$

Work left
$=1-\frac{67}{75}=\frac{8}{75}$

On 17 th day(A + B) will work and they will finish 8/150

$\therefore Workleft=\frac{8}{75}-\frac{8}{150}=\frac{8}{150}=\frac{4}{75}$

On 18th day (A + C) will work and they will finish it in
$\frac{120}{7}\times \frac{4}{75}=\frac{32}{35}days$

$\therefore$ Whole work will be done in
$17\frac{32}{35}days$