# If $m$ men can do a job in $p$ days, then $(m + r)$ men can do the job in how many days?

(A)$(p + r)$days

(B) $\dfrac{{mp}}{{m + r}}$days

(C) $\dfrac{p}{{m + r}}$days

(D) $\dfrac{{m + r}}{p}$days

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**Hint:**To solve this question in detail one should have a deep knowledge of the Unitary method. In this whole solution, we will apply the unitary method many times.

**Complete step by step answer:**

By applying unitary method we can get,

Work done by $m$men in $p$ days$ = 1$ Statement (1)

$\therefore $ Work done by $m$men in $1$ day$ = \dfrac{1}{p}$part Statement (2)

And Work done by $1$man in $1$ day$ = \dfrac{1}{{mp}}$part Statement (3)

Now, we have to find the number of days required to complete the job by $(m + r)$men,

Therefore after statement (3) we can write that,

Work done by $(m + r)$men in $1$ day$ = \dfrac{{(m + r)}}{{mp}}$ part

Now again by applying the unitary method in a different way to find the time taken by $(m + r)$men to do the job,

Time taken by $(m + r)$men to do $\dfrac{{(m + r)}}{{mp}}$part of work$ = 1$ day

$\therefore $ Time taken by $(m + r)$men to do full work (it means$1$)$ = \dfrac{{1 \times 1}}{{(\dfrac{{m + r}}{{mp}})}} = \dfrac{{mp}}{{m + r}}$ days.

Hence $(m + r)$ men can do the job in $\dfrac{{mp}}{{m + r}}$days.

Answer- (B)

**Note:**

Second method-

There is also a formula based method to solve this question,

If ${M_1}$men can do ${W_1}$ work in ${D_1}$ days working ${H_1}$hours per day and ${M_2}$men can do ${W_2}$ work in ${D_2}$ days working ${H_2}$hours per day, then

\[\dfrac{{{M_1}{D_1}{H_1}}}{{{W_1}}} = \dfrac{{{M_2}{D_2}{H_2}}}{{{W_2}}}\]

If you do not have one of these values then put $1$in place of that.