Question

7. If 12 men and 16 boys can do a piece of
work in 5 days and 13 men and 24 boys can
do it in 4 days, compare the daily work
done by a man with that done by a boy.
​

Answer 1

→Let 1 man's 1 days' work be 'x' and 1 boy's 1 days' work be 'y'.

➪ Solution:-

then ;

↪12x+16y=1/5 ... (1)

↪13x+24y=1/4 ... (2)

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Multiplying (1) by 3 and (2) by 2:-

↪36x+48y=3/5 ...(3)

↪26x+48y=1/2 ...(4)

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Subtracting eq. (4) from eq. (3):-

↪

$\frac{3}{5} - \frac{1}{2} = \frac{6 - 5}{10} \\ \\ \frac{1}{10} = x$

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Putting x=1/100 in eq. (1)

$16y = \frac{1}{5} - \frac{12}{100} = \frac{20 - 12}{100} \\ \frac{8}{100} \\ \frac{1}{200} = y$

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Required Ratio= x:y

↪1/100:1/200

↪1:2

Hope it helps✌.