Question

15 men can complete a work in 210 days, They started the work but at the end of 10 days, 15 additional men, with double efficiency, were inducted, How many days in all did they take to finish the work ?

• A. $72\frac{1}{2}$days
• B. $84\frac{3}{4}$days
• C. $76\frac{2}{3}$
• D. 70 days

Answer 1

Answer: (C)

$76\frac{2}{3}$

15 men's 1 days' work = $\frac{1}{210}$ $\therefore$ 15 men's 10 days' work $\frac{10}{210}=\frac{1}{21}$ Remaining work = $1-\frac{1}{21}=\frac{20}{21}$
The additional 15 men's 1 days' work =$1-\frac{2}{210}=\frac{1}{105}$ $\therefore$ These 30 men's 1 days' work = $(\frac{1}{210}+\frac{1}{105})=\frac{1+2}{210}=\frac{3}{210}=\frac{1}{70}$
$\frac{1}{70}th$ of the work can be done in 1 day
$\therefore$ $\frac{20}{21}th$ of the work can be done in $(70\times \frac{20}{21})$ days $=\frac{200}{3}$ days = $66\frac{2}{3}$ days
$\therefore$ Total no. of days = $66\frac{2}{3}$ days + 10 days = $76\frac{2}{3}$ days