Question

Jaya and Seema can together do a piece of work in 10 hours. Seema alone can do it in 15 hours. How long will Jaya take to do it alone?

Answer 1

Hint: We can assume x as the time required to complete the work by Jaya alone. Then the work done per hour by her will be $\dfrac{1}{x}$. The work done per hour by Seema will be the reciprocal of the time she required to complete the work by herself. The sum of the work done per hour of both will be the reciprocal of the time taken to complete the work together. Now we have an equation in x and by solving it, we get the required time.

Complete step by step Answer:

Jaya and Seema can together do a piece of work in 10 hours. Therefore, the total work done together is the reciprocal of the time required to complete it.
Work done by both in an hour is $\dfrac{1}{{10}}$.
Seema alone takes 15 hours to do the same work. So, we can write the work done by Seema alone in an hour as the reciprocal of 15.
Work is done by Seema in an hour $\dfrac{1}{{15}}$
Let us assume the time taken by Jaya to do the work is x hour. Then the work done in an hour by Jaya is the reciprocal of x.
Work is done by Jaya in an hour $\dfrac{1}{x}$
The total work done by both in an hour is the sum of the work done per hour Jaya and Seema separately. So, we can write this as an equation.
\[ \Rightarrow \dfrac{1}{x} + \dfrac{1}{{15}} = \dfrac{1}{{10}}\]
We can subtract both sides with $\dfrac{1}{{15}}$
\[ \Rightarrow \dfrac{1}{x} = \dfrac{1}{{10}} - \dfrac{1}{{15}}\]
After doing the calculation, we get,
\[ \Rightarrow \dfrac{1}{x} = \dfrac{{3 - 2}}{{30}} = \dfrac{1}{{30}}\]
Now we can take the reciprocal on both sides to get the value of x.
\[ \Rightarrow x = 30\]
Therefore, Jaya will take 30 hours to complete the work alone.

Note: We cannot use the time taken directly to solve this problem as it cannot be equated to the total time directly. We can only add their individual work is done per hour or the speed of their work and equate to their combined speed of work. Here we considered the work as a unity. So, the work done in an hour is the reciprocal of the time taken to complete the work. We must be careful while doing calculations with fractions. We can add or subtract the fractions by making its denominator the same.