If 3 men and 4 boys can earn Rs. 2100 in 7 da | vedclass

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Question

(A) Let the daily wage of $1$ man be $m$ and the daily wage of $1$ boy be $b$.From the first condition:$(3m + 4b) 	imes 7 = 2100 \Rightarrow 3m + 4b

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(A) Let the daily wage of $1$ man be $m$ and the daily wage of $1$ boy be $b$.From the first condition:$(3m + 4b) 	imes 7 = 2100 \Rightarrow 3m + 4b = 300$ .....$(i)$From the second condition:$(11m + 13b) 	imes 8 = 8300 \Rightarrow 11m + 13b = 1037.5$ .....$(ii)$Multiply equation $(i)$ by $11$ and equation $(ii)$ by $3$:$33m + 44b = 3300$ .....$(iii)$$33m + 39b = 3112.5$ .....$(iv)$Subtracting $(iv)$ from $(iii)$:$5b = 187.5 \Rightarrow b = 37.5$Substitute $b = 37.5$ into $(i)$:$3m + 4(37.5) = 300 \Rightarrow 3m + 150 = 300 \Rightarrow 3m = 150 \Rightarrow m = 50$Daily earnings of $7$ men and $9$ boys $= 7(50) + 9(37.5) = 350 + 337.5 = 687.5$.Number of days required $= \frac{11000}{687.5} = 16$ days.

If $3$ men and $4$ boys can earn $Rs. 2100$ in $7$ days,and $11$ men and $13$ boys can earn $Rs. 8300$ in $8$ days,in what time will $7$ men and $9$ boys earn $Rs. 11000$? (in days)

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