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Question
The work done by (x – 2) men in (4x + 1) days and the work done by (4x + 1) men in (2x – 3) days are in the ratio 3 : 8. Find the value of x.
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Solution
Assuming that all the men do the same amount of work in one day and one day work of each man = 1 units, we have,
Amount of work done by (x – 2) men in (4x + 1) days
= Amount of work done by (x – 2)(4x + 1) men in one day
= (x – 2)(4x + 1) units of work
Similarly,
Amount of work done by (4x + 1) men in (2x – 3) days
= (4x + 1)(2x – 3) units of work
According to the given information,
`((x - 2)(4x + 1))/((4x + 1)(2x - 3)) = 3/8`
`(x - 2)/(2x - 3) = 3/8`
8x – 16 = 6x – 9
2x = 7
x = `7/2` = 3.5
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