Question

10 men can finish the construction of a hut in 8 days. How many men are needed to finish the same in half day.
(A) 80
(B) 100
(C) 120
(D) 160

Answer 1

Hint: Time and work problems deal with the simultaneous performance involving the efficiency of an individual or a group and the time taken by them to complete a piece of work.
We will use the following formula to solve the above given question.

Formula used: The relation between the number of people working $(M)$, the number of days worked $(D)$, the number of hours worked per day $(H)$ and the quantity of work $(W)$ for two different cases is given below :
$\dfrac{{{M_1} \times {D_1} \times {H_1}}}{{{W_1}}} = \dfrac{{{M_2} \times {D_2} \times {H_2}}}{{{W_2}}}$

Complete step by step answer:
 For condition 1
Total number of men, ${M_1} = 10$
Total number of days, ${D_1} = 8$ days
For condition 2
Let, total number of men $ = {M_2}$
Total working days, ${D_2} = \dfrac{1}{2}$
In given question work is same $({W_1} = {W_2})$
So, by using the relation between M, D and W, we can calculate the number of men ${M_2}$.
$\dfrac{{{N_1} \times {D_1} \times {H_1}}}{{{W_1}}} = \dfrac{{{N_2} \times {D_2} \times {H_2}}}{{{W_2}}}$
or,
${M_1} \times {D_1} = {M_2} \times {D_2}$
$($as ${W_1} = {W_2}$ and we can assume that ${H_1} = {H_2})$
$10 \times 8 = {M_2} \times \dfrac{1}{2}$
${M_2} = 10 \times 8 \times 2$
${M_2} = 160$

Therefore, 160 mens can finish the same work in $\dfrac{1}{2}$ day.

Note: We can solve this problem by a simple method also.
10 men finished in 8 days.
So, to complete the work in 1 day we need $ = 10 \times 8men = 80men$.
So, to complete it in $\dfrac{1}{2}$ day we need $ = $ double of men power doing the work in one day.
i.e., $80 \times 2 = 160men$.