Swapna can do a piece of work in 36 days and Radhika can do the same work in 20 days. Swapna started the work alone. After how many days should Radhika join her so that the work is finished in 27 days?

Given:

Swapna can do the work in 36 days.

Radhika can do the work in 20 days.

Work needs to be finished in 27 days.

Formula used:

LCM method to find total work.

Efficiency = Total work / Number of days.

Calculations:

Let the total work is 180 (LCM of 36 and 20 is 180)

Swapna's efficiency = 180 / 36 = 5 units/day.

Radhika's efficiency = 180 / 20 = 9 units/day.

Let Radhika join after × days.

Swapna works alone for × days, then together for (27 - ×) days.

Total work = (Swapna's work alone) + (Combined work)

180 = 5× + (5 + 9)(27 - ×)

180 = 5× + 14(27 - ×)

180 = 5× + 378 - 14×

180 = 378 - 9×

9× = 378 - 180

9× = 198

× = 198 / 9 = 22

∴ Radhika should join after 22 days.