Question

A and B together can complete a work in 12 days. A alone can complete it in 20 days If B now does the work for half a day dally Then in how many days A and B together will complete the work?
A) 15 days
B) 20 days
C) 45 days
D) 30 days

Answer 1

Hint: A and B can together complete a work in 12 days. Calculate the work done in one day by A and B say x. A alone can complete the work in 20 days. Calculate the work done in one day only by A say y. Subtract y from x to get the amount of work which can be done by B in one day z. Reciprocate z to get the no. of days B alone will take to finish the work say a. If he works half a day then the no. of days will be doubled for B say 2a. Add y and 1/2a to get the required value.

Complete step-by-step answer:
We are given A and B together can complete a work in 12 days.
The work done by A and B together in a day will be $ \dfrac{1}{{12}} $
We are also given A alone can finish the work in 20 days.
The work done by only A in a day will be $ \dfrac{1}{{20}} $
Subtract $ \dfrac{1}{{20}} $ from $ \dfrac{1}{{12}} $ to get the work done by only B in a day.
 $
  B = \dfrac{1}{{12}} - \dfrac{1}{{20}} \\
  B = \dfrac{{5 - 3}}{{60}} = \dfrac{2}{{60}} \\
  B = \dfrac{1}{{30}} \\
  $
Therefore, B alone can finish $ \dfrac{1}{{30}} $ of the work in one day.
This means B alone takes 30 days to finish the total work.
When B works half a day then he will take $ 2 \times 30 = 60 $ days to finish the total work.
When A works full day and B works half day then the work which will be finished in one day will be
 $
   = \dfrac{1}{{20}} + \dfrac{1}{{60}} \\
   = \dfrac{{3 + 1}}{{60}} \\
   = \dfrac{4}{{60}} \\
   = \dfrac{1}{{15}} \\
  $
A and B can together finish $ \dfrac{1}{{15}} $ th of the work in one day, this means when A works full day and B works half day then it takes 15 days to finish the total work.
So, the correct answer is “Option A”.

Note: This is a numerical ability, aptitude question. They are useful in efficient and objective comparisons. If a work is done in n days then the work done in one day will be the reciprocal of n.