Question

27. 8 men can do a piece of work in 12 days. 4
women can do it in 48 days and 10 children
can do it in 24 days. In how many days can
10 men, 4 women and 10 children together
complete the piece of work? (Bank P.O. 2006)
(a) 5 days
(b) 15 days
(c) 28 days
(d) 6 days
(e) None of these​

Answer 1

$\sf\huge\green{\underbrace{Answer\implies option-(d)}}$

$\sf\large\underline\purple{Given:}$

$\rm{\implies 8\:men\:can\:do\:_{(a\:work)}=12\:days}$

$\rm{\implies 4\:women\:can\:do\:_{(a\:work)}=48\:days}$

$\rm{\implies 10\: children\:can\:do\:_{(a\:work)}=12\:days}$

$\sf\large\underline\red{To\: Find:}$

$\rm{\implies work\:done\:by\:_{(10M+4W+10C)}=?\:days}$

$\sf\large\underline\orange{Solution:}$

• At first we have to calculate that how much time to take to complete the work by one man, woman and children, after that we have to calculate work done by them]

$\sf\small\underline\purple{work\:done\:by\:a\:man:}$

$\sf{\implies work\:done\:_{(a\:man)}=Total\:_{(man)}\times\: Total\:_{(days)}}$

$\sf{\implies work\:done\:_{(a\:man)}=8\times\:12}$

$\sf{\implies work\:done\:_{(a\:man)}=96\:days}$

$\sf\small\underline\purple{work\:done\:by\:a\:woman:}$

$\sf{\implies work\:done\:_{(a\:woman)}=Total\:_{(woman)}\times\: Total\:_{(days)}}$

$\sf{\implies work\:done\:_{(a\:woman)}=4\times\:48}$

$\sf{\implies work\:done\:_{(a\:woman)}=192\:days}$

$\sf\small\underline\purple{work\:done\:by\:a\: children:}$

$\sf{\implies work\:done\:_{(a\: children)}=Total\:_{(children)}\times\: Total\:_{(days)}}$

$\sf{\implies work\:done\:_{(a\: children)}=10\times\:24}$

$\sf{\implies work\:done\:_{(a\: children)}=240\:days}$

• Now calculate work done by them]
• Let, one day's work of man=1/96
• Let, one day's work of woman=1/192
• Let, one day's work of children=1/240

$\sf{\implies work\:done\:_{(them)}=\dfrac{Total\:_{(m+w+c)}}{work\:done\:_{(a\:m+w+c)}}}$

$\tt{\implies work\:done\:_{(them)}=\dfrac{10}{96}+\dfrac{4}{192}+\dfrac{10}{240}}$

$\tt{\implies work\:done\:_{(them)}=\dfrac{5}{48}+\dfrac{1}{48}+\dfrac{1}{24}}$

$\tt{\implies work\:done\:_{(them)}=\dfrac{5+1+2}{48}}$

$\tt{\implies work\:done\:_{(them)}=\dfrac{8}{48}}$

$\tt{\implies work\:done\:_{(them)}=\dfrac{1}{6}}$

Hence,

• They can complete the piece of work in 6 days