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If 8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days. Find the time taken by one man alone and that by one boy alone to finish the work.

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140 days ,280 days

200 days 288 days

188 days 295 days

89 days 302 days

answer is A.

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Detailed Solution

Suppose time taken to finish the work by 1 man= x days
Time taken to finish the work by 1 boy = y days.
Then,
1 man's 1 day's work

= \frac{1}{x}

1 boy's 1 day's work

= \frac{1}{y}

So, 1 day work of 8 men's

= \frac{8}{x}

One day work of 12 boy's

= \frac{12}{y}

According to the question 8 men and 12 boys can finish the work= 10 days. So,

10 (\frac{8}{x} + \frac{12}{y}) = 1

\Rightarrow \frac{80}{x} + \frac{120}{y} = 1

…………………………….(i)
Also 6 men with 8 boys can finish the work= 14 days.

So, 14 (\frac{6}{x} + \frac{8}{y}) = 1

\Rightarrow \frac{84}{x} + \frac{112}{y} = 1

……………………………(ii)
Substituted

\frac{1}{x} = u and \frac{1}{y} = v

in equations (i) and (ii)

80 u + 120 v - 1 = 0

………………….(iii)

84 u + 112 v - 1 = 0

…………………..(iv)
Cross-multiplication method,

\frac{u}{- 120 + 112} = \frac{- v}{- 80 + 84}

= \frac{1}{80 \times 112 - 120 \times 84}

\Rightarrow \frac{u}{- 8} = \frac{v}{- 4} = \frac{1}{- 1120}

\Rightarrow u = \frac{- 8}{- 1120}

\Rightarrow u = \frac{1}{140}

And

v = \frac{- 4}{- 1120}

= \frac{1}{280}

Now,

u = \frac{1}{140}

\Rightarrow \frac{1}{x} = \frac{1}{140}

\Rightarrow x = 140

And,

v = \frac{1}{280}

\Rightarrow \frac{1}{y} = \frac{1}{280}

\Rightarrow y = 280

Hence,1 man can finish the work in 140 days and 1 boy can finish the work in 280 days.
Correct option is 1.

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