Sharad can complete a piece of work alone in 13 days and Varad can complete the same piece of work alone in 9 days. They started the work together, but Varad had to leave 11 days before the completion of the work. In how many days will the work complete?​

Correct option is C

Given:

Sharad can complete the work in 13 days

Varad can complete the work in 9 days

Varad leaves 11 days before the work is completed

We need to find the total time (x days) to complete the work

Formula Used:

Work done = Efficiency × Time

Solution: ​

Let the total work = LCM of 13 and 9 = 117 units

Sharad’s efficiency = 117 ÷ 13 = 9 units/day

Varad’s efficiency = 117 ÷ 9 = 13 units/day

Let the total time to complete the work = x days

So Varad worked only for x - 11 days

Sharad worked for full x days

Now total work = Work by Sharad + Work by Varad

117 = 9x + 13(x - 11)

117 = 9x + 13x - 143

117 + 143 = 22x

260 = 22x

x = $$\frac{260}{22}$$​ = 11$$\frac{9}{11}$$​ days