If 10 men and 15 women complete a piece of wo | vedclass

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Question

(C) Let $m$,$w$,and $b$ be the efficiency of a man,a woman,and a boy respectively.
Given: $(10m + 15w) 	imes 8 = (12m + 8w) 	imes 10$
$80m + 120w

Vedclass · Accepted Answer

Quantity $I =$ Quantity $II$

Vedclass · Answer

(C) Let $m$,$w$,and $b$ be the efficiency of a man,a woman,and a boy respectively.
Given: $(10m + 15w) 	imes 8 = (12m + 8w) 	imes 10$
$80m + 120w = 120m + 80w$
$40w = 40m \implies m = w$.
Since a boy is $50\%$ less efficient than a man,$b = 0.5m$,which means $m = 2b$.
Total work = $(10m + 15m) 	imes 8 = 25m 	imes 8 = 200m$ units.
Quantity $I$: $2m + 4w + 18b = 2m + 4m + 9m = 15m$. Time = $200m / 15m = 40/3$ days.
Quantity $II$: $9m + 3w + 6b = 9m + 3m + 3m = 15m$. Time = $200m / 15m = 40/3$ days.
Therefore,Quantity $I =$ Quantity $II$.

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