Question

A takes 49 days more than C and 45 days more
than B to complete a work. C takes as much time
as A and B together to complete the work. In how
many days A and B together will complete the
work?​

Answer 1

Consider the time taken by C is x days,

So, the time taken by A = (x+49) days,

And, time taken by B = (x+49) - 45 = (x+4) days ( ∵ A takes 45 days more than B).

Thus, in one day,

Work done by C = $\frac{1}{x}$

Work done by A = $\frac{1}{x+49}$

Work one by B = $\frac{1}{x+4}$

If C takes as much time as A and B together to complete the work,

Then, the one work day of C is equal to combined one day work of A and B.

That is,

                      $\frac{1}{x}=\frac{1}{x+49}+\frac{1}{x+4}$

                      $\frac{1}{x}=\frac{x+4+x+49}{x^2+4x+49x+196}$

                     $\frac{1}{x}=\frac{2x+53}{x^2+53x+196}$

$x^2+53x+196=2x^2+53x$

                   $x^2=196$

                    $x=14$       (∵ Days can not be negative)

Therefore, the time taken by A and B together would be 14 days.