Question

Previous Gupta and Kiran can do a work in 15 days and 30 days respectively. They both work for 3 days and then Gupta leaves. In how many days is the remaining work completed by Kiran?

Answer 1

Answer: 21 days

Step-by-step explanation:

Since, Gupta can do work in 15 days when he works alone,

Therefore, the work done in one day by Gupta when he works alone(his efficiency) = $\frac{1}{15}$

Similarly, the work done in one day by Kiran when he works alone(his efficiency) = $\frac{1}{30}$

⇒ Total work done by both in one day when they work simultaneously  

= $\frac{1}{15} + \frac{1}{30} = \frac{2}{30} + \frac{1}{30} = \frac{3}{30} = \frac{1}{10}$

⇒ Total work done by both in 3 days when they work simultaneously

= $\frac{3}{10}$

Remaining part of work = $1 - \frac{3}{10} = \frac{10 - 3}{10} = \frac{7}{10}$

$Time = \frac{work}{efficiency}$

Therefore, the time taken by Kiran in remaining part of work = $\frac{7/10}{1/30} = \frac{210}{10} = 21$

⇒ Kiran will take 21 days to complete the remaining work.