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A is 20% less efficient than B. If B alone can do the work in 40 days then in how many days A and B can together complete the same work?

The above question is from made easy test series.

Sol:

Given B alone can do the work in 40 days

B’s one day work is 1/40

As A is 20% less efficient

So, A’s work one day work is $\frac{1}{40}$x $\frac{80}{100}$ = $\frac{1}{50}$

So A alone can do the same work in 50 days.

A’s and B’s one day combined work =  $\frac{1}{40}$+ $\frac{1}{50}$ = $\frac{9}{200}$

Hence A and B together can complete the work in 22.22 days

My Doubt:

Here A is 20% less efficient than B therefore  $\frac{Work \ done \ by\ B}{Work \ done \ by\ A}$= $\frac{100}{80}$ = $\frac{5}{4}$

But why it can’t be like $\frac{Work \ done \ by\ B}{Work \ done \ by\ A}$= $\frac{120}{100}$ = $\frac{6}{5}$ as this also implies that A is 20% less efficient

Correct me if I am wrong.

Is there a way to decide when to use which method?

20% of 120 is 24. Word done by A will be less than work done by B by 24.

So in your doubt, the second equation should be $\frac{120}{120-24} = \frac{120}{96} = \frac{5}{4}$

Thank you @DebSujit I got it now