Delhi Police Constable Exam Model Paper 3

Given:
20 builders can excavate a building in 50 days.
Formula used:
(M1 × D1)/W1 = (M2 × D2)/W2, where M = Number of workers, D = Number of days and W = work
Calculation:
Let total work be 50unitsEfficiency of 20 builders = 50/50 = 1 units/day
After 10 days, 20 more builders join them, that is 40 builders work after 10 days
Work left after 10 days = 50 - 10 = 40 units
Let the required number of days be D
$\frac{\left(20\times 10\right)}{10}=\left(20+20\right)\times \frac{\mathit{D}}{40}$
⇒ $20\times 40=40\times \mathit{D}$
⇒ $\mathit{D}=20$ days
Alternate Method
Let 1 builder do 1 unit/day work.
Hence, total work = $20\times 50\times 1=1000$ units
Work done by 20 builders in 10 days = 20 × 10 = 200 units
Now, remaining work = $1000-200=800$ units
∴ Required time = $\frac{800}{\left(20+20\right)}=\frac{800}{40}=20$ days.