Question

5 men and 2 women can complete a work in 4 days while 6 men and 3 women can complete their work in 3 many days how many days will the work be completed by 1 men alone and 1 woman alone

Answer 1

Let the work done by 1 man in 1 day be 1/x and let the work done by 1 woman in 1 day be 1/y.
⇒By the condition,
$\frac{5}{x} + \frac{2}{y}= \frac{1}{4}$
⇒4xy * $\frac{5}{x}$ + 4xy* $\frac{2}{y}$ =4xy*$\frac{1}{4}$
⇒20y+8x=xy........(1)
and,
$\frac{6}{x} + \frac{3}{y} = \frac{1}{3}$
⇒3xy * $\frac{6}{x}$ + 3xy * $\frac{3}{y}$ =3xy *$\frac{1}{3}$
⇒18y+9x=xy
 substituting xy as 20y+8x we get:
18y+ 9x=20y+8x
⇒x=2y.
Now we have:
$\frac{5}{2y} + \frac{2}{y} = \frac{1}{4}$
⇒Multiplying each term of the equation with 4y (LCM) we get:
10+8=y
y=18 , x=36.
Solution: 1/18 + 1/36
=3/36 's reciprocal=12.
Ans:The required no of days is 12.