Question

If 20 men working 7hours a day can do a piece of work in 10 days, in how many days will 15 men working 8 hours a day do the same piece of work?
\[
  A.{\text{ 15}}\dfrac{5}{{21}} \\
  B.{\text{ 11}}\dfrac{2}{3} \\
  C.{\text{ }}6\dfrac{9}{{16}} \\
  D.{\text{ 4}}\dfrac{1}{5} \\
 \]

Answer 1

Hint- We will solve the problem by unitary method. First find out the work done by a unit worker or one worker in a unit hour or one hour. And then find the given number of workers and given number of hours.

Complete step-by-step answer:

Given that: 20 men working 7 hours a day can complete the work in 10 days.
So, 20 men working 1 hour a day can complete the work in $\left( {10 \times 7} \right)$ days (less hours implies more days)
So, 1 man working 1 hour a day can complete the same work in $\left( {10 \times 7 \times 20} \right)$ days (less men implies more days)
Similarly 1 man working 8 hours a day can complete the work in $\dfrac{{\left( {10 \times 7 \times 20} \right)}}{8}$ days (more hours implies less days)
And finally 15 men working 8 hours a day can complete the work in $\dfrac{{\left( {10 \times 7 \times 20} \right)}}{{8 \times 15}}$ days (more men implies less days)
Simplifying the number of days:
No of days $ = \dfrac{{\left( {10 \times 7 \times 20} \right)}}{{8 \times 15}} = \dfrac{{35}}{3} = 11\dfrac{2}{3}$
Hence, 15 men working 8 hours a day can complete the same work in $11\dfrac{2}{3}$ days.
So, option B is the correct option.

Note- The problem related to work and time as above can also be solved by the method of proportion. But the method used above is the basic method based on the unitary method. In the unitary method we find the work done for unit days and by unit worker and find for overall work.