Question

45. 10 men can dig a pit in 29 days. If a man works
half as much as a boy, then 5 men and 12 boys
can dig it in
(A) 10 days
(B) 15 days
(C) 12 days
(D) 14 days​

Answer 1

=> Answer => Option - (A)

$\sf\small\underline\blue{Given:-}$

$\sf{\implies 10\:men\:can\:dig\:a\:pit = 29\:days}$

$\sf{\implies A\:man\:work\:half\:work= A\:boy's\:work}$

$\sf\small\underline\blue{To\: Find:-}$

$\sf{\implies 5\:men\:and\:12\:boys\:can\:dig=?}$

$\sf\small\underline\blue{Solution:-}$

To calculate the word done by them at first we have to find out word by a man and boys then calculate work by 5 men and 12 boys.

$\sf\small\underline\red{Let's\: calculate\:now:-}$

$\tt{\implies word\:done\:_{(by\:a\:man)}=\dfrac{work}{men*days}}$

$\tt{\implies Work\:done\:_{(by\:a\:man)}=\dfrac{1}{10*29}}$

$\tt{\implies Work\:done\:_{(by\:a\:man)}=\dfrac{1}{290}}$

$\tt{\implies Work\:done\:_{(by\:a\:boy)}=\dfrac{1}{290\div\:2}}$

$\tt{\implies Work\:done\:_{(by\:a\:boy)}=\dfrac{1}{145}}$

Now calculate work done by 5 men and 12 boys:-

$\tt{\implies work\:done\:_{(by\:them)}=5\:men's\:work + 12\:boys\: work}$

$\tt{\implies work\:done\:_{(by\:them)}=\dfrac{5}{290}+\dfrac{12}{145}}$

$\tt{\implies work\:done\:_{(by\:them)}=\dfrac{5+24}{290}}$

$\tt{\implies work\:done\:_{(by\:them)}=\dfrac{29}{290}}$

$\tt{\implies work\:done\:_{(by\:them)}=\dfrac{1}{10}}$

$\sf\large{Hence,}$

$\bf{\implies work\:done\:_{(5m+12B)}=10\:days}$

Answer 2

Step-by-step explanation:

Given That :-

Total Work Done = 29 day * 10 men = 290

10M = 29 days

B = 2 M

So Acc. to Question ⁉️

= > 5 M + 12 B = 290 ( Total Work )

= > 5 M + 12 * 2 M = 290

= > 29 M = 290

M = 10 days ✅

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