Question

25 জন লোক ও 10 জন বালক একটি কাজ 6 দিনে করে অন্যদিকে 21 জন লোক ও 30 জন বালক ঐ কাজটি 3 দিনে করে কত জন বালক 23 জন লোকের সাথে ওই কাজটি 4 দিনে করবে?​

Answer 1

Given:

25 জন লোক ও 10 জন বালক একটি কাজ 6 দিনে করে অন্যদিকে 21 জন লোক ও 30 জন বালক ঐ কাজটি 5 দিনে করে কত জন বালক 23 জন লোকের সাথে ওই কাজটি 4 দিনে করবে?​

25 men with 10 boys can do in 6 days as much work as 21 men with 30 boys can do in 5 days. How many boys must help 23 men to do the same work in 4 days?

To find:

How many boys must help 23 men to do the same work in 4 days?

Solution:

Let,

"M" → the amount of work done by 1 man in 1 day

"B" → the amount of work done by 1 boy in 1 day

25 men with 10 boys can do in 6 days as much work as 21 men with 30 boys can do in 5 days. So we can form the equation as,

$(25M + 10B )6 = (21M + 30B) 5$

$\implies 150M + 60B = 105M + 150B$

$\implies 45M = 90B$

$\implies M = 2B \:. . . . (1)$

Let "x" be the required no. of boys.

Therefore, we can form an equation as:

$(23M + xB)4 = (25M + 10B)6$

on substituting from (1), we get

$\implies (46B + xB)4 = (50B + 10B)6$

$\implies (46B + xB)4 = (60B )6$

$\implies 46B + xB = 360B\times \frac{1}{4}$

$\implies 46B + xB = 90B$

$\implies xB = 44B$

$\implies \bold{x = 44}$

Thus, 44 boys must help 23 men to do the same work in 4 days.

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