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Question
Choose the most appropriate option.
Two men and seven boys can do work in 14 days. Three men and eight boys can do the same work in 11 days. Further, eight men and six boys can do three times the amount of this work in:
Options
18 days
21 days
30 days
24 days
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Solution
21 days
Explanation:
According to question
(2 × 14) men + (7 × 14) boys = (3 × 11) men + (8 × 11) boys
⇒ 5 men = 10 boys or 1 man = 2 boys
∴ (2 men + 7 boys) = (2 × 2 + 7) boys = 11 boys
(8 men + 6 boys) = (8 × 2 + 6) boys = 22 boys
Let the required number of days be x
According to the ratio proportion,
Boys 22: 11 Work 1: 3] :: 14 : x
∴ (22 × 1 × x) = (11 × 3 × 14)
`∴"x"=462/22=21`
Hence, the required number of days = 21.
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