Question

If 5 men or 9 women can do a piece of work in 19 days then in how many days will 3 men and 6 women do the same work?
(A) 12 days
(B) 15 days
(C) 18 days
(D) 21 days.

Answer 1

Hint:
Find the number of days 1 man and 1 woman take to do the work. Then by using the method of inverse proportion i.e.\[\dfrac{{{\text{M}}_{\text{1}}}{{\text{D}}_{\text{1}}}}{{{\text{W}}_{\text{1}}}}=\dfrac{{{\text{M}}_{\text{2}}}{{\text{D}}_{\text{2}}}}{{{\text{W}}_{\text{2}}}}\]
find the required number of days using this formula.

Complete step by step solution:
It is given that 5 men or 9 women can do the job in 19 days.
So,
⇒ 5 men $=$ 9 women
⇒ 1 man $=\dfrac{9}{5}$ women
then,
⇒ 3 men $=3\left( \dfrac{9}{5} \right)$ women
So,
Work done $=3\ \text{men}+6\ \text{women}$
⇒ Work done $=3\left( \dfrac{9}{5} \right)+6$
⇒ Work done $=\dfrac{27}{5}+6=\dfrac{57}{5}$
Now,
According to the question,
\[\dfrac{{{\text{M}}_{\text{1}}}{{\text{D}}_{\text{1}}}}{{{\text{W}}_{\text{1}}}}=\dfrac{{{\text{M}}_{\text{2}}}{{\text{D}}_{\text{2}}}}{{{\text{W}}_{\text{2}}}}\]
Let ${{\text{D}}_{\text{2}}}$ be x
$\Rightarrow \dfrac{9\times 19}{{{\text{w}}_{\text{1}}}}=\dfrac{\dfrac{57}{5}\times x}{{{\text{w}}_{\text{2}}}}$
The work done will be the same so it will be canceled out.
$\Rightarrow 9\times 19=\dfrac{57x}{5}$
⇒ After cross-multiplication, we get
$\Rightarrow 3=\dfrac{x}{5}$
$\Rightarrow x=15\ \text{days}\text{.}$

Note:
This is a time and work question based on inverse proportion. When the number of people decreases, then the number of days increases.