Question

If A works in 22 days and B completes it in 33 days.If A left work before 3 days then in how many days total work will complete.

Answer 1

The total work will be completed in 15 days.

Explanation

A completes a work in 22 days and B completes it in 33 days.

So, A works in 1 day $= \frac{1}{22}$ and B works in 1 day $=\frac{1}{33}$

Suppose, the total work will be completed in $x$ days.

As,  A left work before 3 days , that means B will work alone for the last 3 days and together works for $(x-3)$ days.

So, the equation will be......

$(\frac{1}{22}+\frac{1}{33})(x-3)+(\frac{1}{33})*3 =1\\ \\ \frac{5}{66}(x-3) +\frac{1}{11}=1\\ \\ 66[\frac{5}{66}(x-3) +\frac{1}{11}]=66\\ \\ 5(x-3)+6=66\\ \\ 5(x-3)=60\\ \\ x-3=12\\ \\ x=15$

Thus, the total work will be completed in 15 days.