Question

Ten men, working for 6 days of 10 hours each, finish $\frac{5}{21}$ of a piece of work. How many men working at the same rate and for the same number of hours each day, will be required to complete the remaining work in 8 days?

• A. 24
• B. 26
• C. 25
• D. 21

Answer 1

The correct option is A 24

Lets first find the number of working hours required to complete $\frac{5}{21}$ of the work.
M = number of men
D = number of days
H = number of hours worked per day
N = work done
MDH = N
10$\times$6$\times$10 = $\frac{5}{21}$
600 hours to complete $\frac{5}{21}$ of work
Let the total number of hours required to complete the work be $x$ then
$x$ = $\frac{5}{21}$ $÷$600
= 600$\times$$\frac{21}{5}$
$x$ = 2520 hours
so the remaining work is $x$$-$ $\frac{5}{21}$
= $\frac{16}{21}$ $x$
=$\frac{16}{21}$$\times$2520
= 1920 hours required to complete remaining $\frac{16}{21}$ of the work
now the equation we get is
MDH = N
MDH = 1920
M $\times$ 8$\times$10 = 1920
M = $\frac{1920}{80}$
M = 24
Ans. 24 men