Question : Some carpenters promised to complete the work in 20 days. When the work was started, 8 of them were absent and the remaining completed the work in 40 days. What was the original number of carpenters?
Option 1: 18
Option 2: 12
Option 3: 10
Option 4: 16
Correct Answer: 16
Solution :
Number of days promised, $D_1$ = 20 days
Number of days taken to complete the work, $D_2$ = 40
Let the number of carpenters($M_1$) be $x$
Absent carpenters = 8
Remaining carpenters($M_2$) = $(x-8)$
We know that,
$M_1D_1= M_2D_2$
⇒ $x\times20=(x-8)\times40$
⇒ $20x=40x-320$
⇒ $20x=320$
⇒ $x=16$
Hence, the correct answer is 16.
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