Question

If 24 workers can build a wall in 15 days, how days will 8 workers take to build a similar wall?
a. 42 days
b. 45 days
c. 48 days
d. None of these

Answer 1

Hint: Here, we have the data that 24 workers are building a wall in 15 days, we have to find the number of days will 8 workers take to build a similar wall. We will use the formula $\dfrac{{{M}_{1}}{{D}_{1}}{{H}_{1}}}{{{W}_{1}}}=\dfrac{{{M}_{2}}{{D}_{2}}{{H}_{2}}}{{{W}_{2}}}$ , where M is number of men, D is number of days, H is number of hours per day and W is work done. We have to consider only M and D here. We have ${{M}_{1}}=24,{{D}_{1}}=15,{{M}_{2}}=8$ , substituting these we can find ${{D}_{2}}$ .

Complete step-by-step answer:
We will be using the manpower-time-work concept. According to this, we have $\dfrac{MDH}{W}=\text{constant}$ , where M is number of men, D is number of days, H is number of hours per day and W is work done. When we have two conditions given, this formula is extended as $\dfrac{{{M}_{1}}{{D}_{1}}{{H}_{1}}}{{{W}_{1}}}=\dfrac{{{M}_{2}}{{D}_{2}}{{H}_{2}}}{{{W}_{2}}}$ .
In our question, we have to relate only the M and D terms since the rest, i.e H and W are the same for building a similar wall.
Since we have been given that 24 workers can build in 15 days, we can write that ${{M}_{1}}=24,{{D}_{1}}=15$.
Now, let us take the number of days which 8 workers will take to make a similar wall to be $\alpha $ . So, we can write that as ${{M}_{2}}=8,{{D}_{2}}=\alpha $ .
Now applying the above formula, we have
$24\times 15=8\times \alpha $
$\Rightarrow \alpha =\dfrac{24\times 15}{8}$$=\dfrac{360}{8}=45$
Hence, 8 workers take 45 days to build the similar wall.

So, the correct answer is “Option b”.

Note: There is a high possibility that students might apply the concept of unitary method for this question. So, they may consider that 1 worker will build in $\dfrac{15}{24}$ days, so, for 8 workers, the number of days will be $\dfrac{15}{24}\times 8=5$ days. But, this is not correct logically, how can less number of workers finish the same work in less number of days since other conditions are not changing. Do not make this mistake. So, for such questions, always use the work-time concept.