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IT was estimated that $52$ men can complete a strip in a newly constructed highway connecting cities $P$ and $Q$ in $10$ days, Due to an emergency, $12$ men were sent to another project. How many number of days, more than the original estimate, will be required to complete the strip?

  1. $3$ days
  2. $5$ days
  3. $10$ days
  4. $13$ days
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Migrated from GO Mechanical 2 years ago by Arjun

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If $M_{1}$ number of people can do $W_{1}$ work, in $D_{1}$ days, working $T_{1}$ hours each day and the $M_{2}$ number of people can do $W_{2}$ work, in $D_{2}$ days, working $T_{2}$ hours each day, then the relation between them will be
$$ \dfrac{M_{1} \times D_{1} \times T_{1}}{W_{1}} = \dfrac{M_{2} \times D_{2} \times T_{2}}{W_{2}} $$
Now, $52 M \times 10 D = 40 M \times xD$

$\implies x = 13$ days.

The number of days, more than the original estimate, that will be required to complete the strip $ = 13 – 10 = 3$ days.

So, the correct answer is $(A).$
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