Question

ram takes 3 days more than rahim to complete a certain work. if they both work together, they complete the work in 2 days. find the no. of days taken by them to complete the work alone​

Answer 1

Answer:

let Rahim takes x days to complete the work.

then Ram will take x+3 days to complete then Ram complete

$\frac{1}{x + 3}$

part of the work in 1 day.

then Rahim complete

$\frac{1}{x}$

part of the work in 1 day

then,

$\frac{1}{x} + \frac{1}{x + 3} = \frac{1}{2}$

$\frac{x + x + 3}{x(x + 3)} = \frac{1}{2}$

$2(2x + 3) = {x}^{2} + 3x$

$4x + 6 = {x}^{2} + 3x$

${x}^{2} - x - 6 = 0$

${x}^{2} - 3x + 2x - 6 = 0$

$x(x - 3) + 2(x - 3) = 0$

$(x - 3)(x + 2) = 0$

then

x=3 or x=-2

we take positive once

then reahim takes 3 days

and ram takes 6 days