Pooja, Neha, and Manoj can do a piece of work in 16, 22, and 20 days respectively. On which day will the work get finished if Pooja is assisted by both Neha and Manoj on every second day?

Data:

Work rates of Pooja (Wp), Neha (Wn), and Manoj (Wm) = 1/16, 1/22, 1/20 work/day respectively

Concept:

On the first day, only Pooja works. On the second day, all three work together.

This pattern repeats.

The total work done on each two-day cycle is the sum of the work done by each person.

Solution:

Calculate the LCM of 16, 22, and 20 to represent the total work.

⇒ LCM of 16, 22, and 20 = 880 units

Calculate the one-day work for Pooja, Neha, and Manoj respectively.

⇒ Pooja's one day work = 880/16 = 55 units

⇒ Neha's one day work = 880/22 = 40 units

⇒ Manoj's one day work = 880/20 = 44 units

Pooja works alone every alternate day and with Neha and Manoj on the other days.

⇒ Work done in two days when Pooja is assisted by Neha and Manoj,

⇒ Pooja's one day work + Neha's one day work + Manoj's one day work + Pooja's one day work

⇒ Work done in two days = 55 + 40 + 44 + 55 = 194 units

Double the days until the remaining work is less than the two-day work.

⇒ Number of such two-day work segments = (880/194) = 4 (since 4 × 194 = 776, which is less than 880)

⇒ Days taken = 2 × 4 = 8 days for 776 units of work

Now 880 - 776 = 104 units of work is left,

Pooja works on the 9th day and completes 55 units, leaving 49 units.

On the 10th day, Pooja, Neha, and Manoj together can complete the remaining work as,

⇒ 55 + 40 + 44 = 139 units > 49 units.

Therefore, the work will be finished on the 10th day.