Question

Harpal is thrice as good as workman as Kewal and takes $10$ days less to do a piece of work than Kewal takes, then Kewal can do that work in:
A) $8$ days
B) $12$ days
C) $13$ days
D) $15$ days

Answer 1

Hint:The given problem is depending upon work as well as efficiency. We will use the formula by comparing the efficiency of the two workers and how much time each individual takes to complete the work. The efficiency of the two workers will be the point which we will use to calculate the final answer.

Complete step-by-step answer:
It is given that Kewal takes 10 days more to complete the piece of work than Harpal does.
The efficiency of Harpal is three times better than Kewal.
That means Kewal takes more time to finish the work than Harpal.
Let us assume that same amount of work to be done by both the candidates individually.
Let us assume that Kewal takes $x$ days to finish the work.
As Harpal takes $10$ days less, he will take $\left( {x - 10} \right)$ days to finish the same piece of work.
Now it is given that Harpal is thrice as good as Kewal. That means efficiency of Harpal is three times better than that of Kewal.
On comparing efficiencies, we can write the following equation:
$\dfrac{x}{3} = \left( {x - 10} \right)$
Simplifying the above equation, we get
$x = 3x - 30$
Therefore, we will solve the above equation for $x$ .
$x = 15$
Thus, Kewal can do that work in $15$ days.

So, the correct answer is “Option D”.

Note:Note that from the given data we had directly given the amount of time both take to finish the work. To compare the remaining part, we used the efficiency of both the workers. We can substitute the values obtained in the given data to verify the result.