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Question

# If (x+4) men can do a piece of work in (x+3) days, then find the number of days that (x+2) men will take for the same work.

A
(x2+7x+8)(x+4) days
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B
(x2+9x+12)(x+2) days
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C
(x2+7x+12)(x+2) days
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D
(2x2+5x+12)(x+2) days
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Solution

## The correct option is C (x2+7x+12)(x+2) daysGiven, (x+4) men can do a piece of work in (x+3) days. We know that if the number of men increase, then the number of days taken to finish the piece of work will be less. Number of men(m)∝1Number of days(d) ∴m1m2 = d2d1 Given, m1 = (x+4) men m2 = (x+2) men d1 = (x+3) days and d2=Number of days taken by (x+2) men ⇒(x+4)(x+2) = d2(x+3) ⇒d2 = (x+4)×(x+3)(x+2) ⇒d2 = (x2+7x+12)(x+2) days

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