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Time and Work

8 men can dig...

Question

$8$ men can dig a pit in $20$ days. If a man works one and a half as much again as a boy, then $4$ men and $8$ boys can dig it in

A

10 d a y s

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B

12 d a y s

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C

15 d a y s

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D

16 d a y s

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Solution

The correct option is B $16 d a y s$
$\begin{matrix} f r o m t h e g i v e n d a t a w o r k d o n e b y m e n = 1 + \frac{1}{2} w o r k d o n e b y b o y = 1 S o, r a t i o o f w o r k d o n e b y m a n a n d b o y = 3 : 2 N o w, T o t a l w o r k = 8 \times 3 \times 20 N o w, 4 m e n + 9 B o y = 4 \times 3 + 9 \times 2 = 12 + 18 = 30 H e n c e, N o . o f d a y s = \frac{8 \times 3 \times 20}{30} = 16 d a y s H e n c e, o p t i o n D i s t h e c o r r e c t a n s w e r . \end{matrix}$

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