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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. - Mathematics

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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.

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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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Exercise 7(A) | Q: 13 | Page no. 87
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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. Concept: Ratios.
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