Question

5 men and 6 boys finish a piece of work in 4 days; 4 men and 3 boys in 6 days. In how many days would 3men and 6 boys finish the same work

Answer 1

15

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Answer 2

Answer:

$5$ days to finish the same work.

Step-by-step explanation:

Given:

$5$ men and $6$ boys finish work in $4$ days, $4$ men and $3$ boys in $6$ days.

Find:

In how many days would $3$ men and $6$ boys finish the same work.

Solution:

According to the question,

$(5m+6b)\times 4=(4m+3b)\\10m+12b=12m+9b\\12b-9b=12m-10m\\3b=2m\\\frac{b}{m}=\frac 23$

So, the efficiency of boys: men $=2:3$

Now, find total work

$(5 \times 3+6 \times 2)\times 4=(15+12) \times 4\\27\times 4=108 total work$

Now, No. of days is $= \frac {total work}{efficiency}$

$=\frac {108} {3\times 3+6 \times 2}$

$=\frac{108}{9+12}=\frac{108}{21}$

$=5 days$

#SPJ2