Question

5. A and B together can do a piece of work in 10 days, but A alone can do it in 15 days. How many days would B alone take to do the same work​

Answer 1

Answer:

30 days

Step by step explanation: If you have been given the number of days taken by a person to work, then his one day's work is reciprocal of number of days.

One day work of A and B = 1/10

One day work of A= 1/15

Therefore, one day work of B= 1/10 - 1/15 = 1/30

Therefore, 30 days.

Answer 2

Given:

The total number of days taken by A and B together to complete the work is 10 days.

The Number of days in which A alone can complete the work is 15 days.

To Find :

We have to find the number of days for which B alone can take to do the same work.

Solution:

Let x be the number of days taken by B alone to complete the same work.

∵ B alone will complete  $\frac{1}{x}$ part of the work in one day.

⇒ A alone will complete $\frac{1}{15}$ part of the work in one day.

⇒ The total number of days taken by A and B together to complete the work is 10 days.

∴ The quantity of work that A and B together can complete in one day is given by,

                 $\[\begin{array}{l}\frac{1}{{15}} + \frac{1}{x} = \frac{1}{{10}}\\\\\frac{1}{x} = \frac{1}{{10}} - \frac{1}{{15}}\\\\\frac{1}{x} = \frac{1}{{30}}\end{array}\]$

            $\[\therefore \,\,x = 30\,\,days\]$

Hence, the total number of days taken by B alone to complete the work is 30 days.