Question

3 men and 2 women can do a piece of work in 15 days.2 men and 3 women can do the same work in 18 days.The number of days taken by 1 woman and 1 man to do the wok in?​

Answer 1

Answer:

x=3,y=6

Step-by-step explanation:

let the work done by men be x days

let the work done by women be y days

then,

work done in one day by one man =1/x

work done in one day by one women=1/y

so,

work done by 3 men in one day=3/x

work done by 2 women in one day=2/y

3/x+2/6=1/15----------(1)

similarly,

work done by 2 men in one day=2/x

work done by 3 women in one day=3/x

we get,

2/x+3/y=1/18-----------(2)

by solving this equation we'll get the value of x & y

Answer 2

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

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

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

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

$\sf{\implies work\:done\:_{(3m+2w)}=15\:days}$

$\sf{\implies work\:done\:_{(2m+3w)}=18\:days}$

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

$\sf{\implies work\:done\:_{(separately\:by\:them)}=?}$

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

We will solve this question by helping linear equation with two variables. As given in the question 3 men and 2 women can do a piece of work in 15 days.2 men and 3 women can do the same work in 18 days.The number of days taken by 1 woman and 1 man to do the work.

$\sf\small\underline\blue{Calculation\:for\:1st\:eq:-}$

$\sf{\implies 3men+2women=\dfrac{1}{15}}$

$\sf{\implies 3m+2w=\dfrac{1}{15}-----(i)}$

$\sf\small\underline\blue{Calculation\:for\:2nd\:eq:-}$

$\sf{\implies 2men+3women=\dfrac{1}{15}}$

$\sf{\implies 2m+3w=\dfrac{1}{18}-----(ii)}$

• By Solving equation (i) and (ii) :-

$\sf{\implies 6m+4w=\dfrac{2}{15}}$

$\sf{\implies 6m+6w=\dfrac{3}{18}}$

• By solving we get :-

$\sf{\implies -2w=\dfrac{2}{15}-\dfrac{3}{18}}$

$\sf{\implies -2w=\dfrac{12-15}{90}}$

$\sf{\implies -2w=-\dfrac{3}{90}}$

$\sf{\implies 2w=\dfrac{1}{30}}$

$\sf{\implies w=\dfrac{1}{60}}$

• Putting the value of w in eq (ii):-

$\sf{\implies 3m+2(1/60)=\dfrac{1}{15}}$

$\sf{\implies 3m+\dfrac{1}{30}=\dfrac{1}{15}}$

$\sf{\implies 3m=\dfrac{1}{15}-\dfrac{1}{30}}$

$\sf{\implies 3m=\dfrac{2-1}{30}}$

$\sf{\implies 3m=\dfrac{1}{30}}$

$\sf{\implies m=\dfrac{1}{90}}$

$\sf\large{Hence,}$

$\sf{\implies work\:done\:_{(a\:man)}=90\:days}$

$\sf{\implies work\:done\:_{(a\:woman)}=60\:days}$