Question

A can do a piece of work in 24 days. If B is 60% more efficient than A. Then the number of days required by B to do the twice as large as the earlier work is
(a) 24
(b) 36
(c) 15
(d) 30

Answer 1

Hint: We are given the efficiency of B with respect to the efficiency of A. We will calculate the number of days required by B to do the same work that A completed in 24 days. We will use the efficiency for this. Then we will calculate the number of days required by B to complete a piece of work which is twice as large as the earlier work.

Complete step by step answer:We have to find the number of days B will take to finish a work that is twice as big as the earlier one.
If a person can do a work in $x$ days, then, we can say that in 1 day that person can do $\dfrac{1}{x}$ amount of work. Hence, work done by A in a day is $\dfrac{1}{24}$.
We will now find the number of days required by B to do the same work as A. We know that B is 60% more efficient than A. So, the amount of work done by B in one day can be calculated as follows,
Work done by B in 1 day $=\dfrac{1}{24}+\dfrac{60}{100}\times \dfrac{1}{24}=\dfrac{10}{240}+\dfrac{6}{240}=\dfrac{16}{240}=\dfrac{1}{15}$.
Therefore, the number of days required by B to complete the same quantity of work as A is 15 days.
Now, we are asked to find the number of days B will take to do a work which is twice as large as the earlier one. So, we will multiply the days taken by B to finish the earlier work by 2.
We know that the number of days required by B to finish the original work is 15 days. So, to finish a work which is 2 times the previous work is $15\times 2=30$. Hence, B will take 30 days to do the new work.

So, the correct answer is “Option d”.

Note: The important part in this type of question is to understand the relation between the quantity of work and the required time to complete it. Using this, we will be able to compare the time taken by different people to do the same work. It is essential that we have a clear idea of what is being asked in the question. It is possible that we might select option (c), since it is the time required by B to do the original work. But we are asked to find the time needed by B to complete double the quantity of original work.