Question

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Answer 1

$\huge\underline\mathcal\purple {Solution}$

Let a man can finish the work in x days and a boy can finish the work in y days .

• Work done by one man in one day

$= \frac{1}{x}$

• Work done by one boy in one day

$= \frac{1}{y}$

According to the que ...

$\frac{2}{x} + \frac{7}{y} = \frac{1}{4} .........(i)$

$\frac{4}{x} + \frac{4}{y} = \frac{1}{3} ........(ii)$

Let ,

$\frac{1}{x} = a$

and

$\frac{1}{y} = b$

Then ,

$2a + 7b = \frac{1}{4} .......(iii)$

$4a + 4b = \frac{1}{3} .......(iv)$

Multiplying eqn. (iii) by 2 and then subtract eqn. (iv) from it

$4a + 14b = \frac{1}{2} .......(v)$

$4a + 4b = \frac{1}{3}$

________________

$10b = \frac{1}{6} = > b = \frac{1}{60}$

$keeping \: b = \frac{1}{60} in \: eqn \: (iii)$

$2a + 7 \times \frac{1}{60} = \frac{1}{4}$

$= > 2a = \frac{1}{4} - \frac{7}{60} = \frac{15 - 7}{60}$

$= > 2a = \frac{8}{60}$

$= > a = \frac{1}{15} = \frac{1}{x} = > x = 15$

Also ,

$b = \frac{1}{60} = \frac{1}{y} = > y = 60$

• A man takes 15 days to do the work alone and a boy takes 60 days to do the work alone .

Answer 2

Step-by-step explanation:

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