Isha can do a certain piece of work in 24 days. Isha and Smriti can together do the same work in 20 days, and Isha, Smriti and Ashlesha can do the same work together in 12 days. In how many days can Isha and Ashlesha do the same work together?​

Correct option is B

Given:

Isha can do the work in 24 days.

Isha + Smriti can do the work in 20 days.

Isha + Smriti + Ashlesha can do the work in 12 days.

Find the time taken by Isha + Ashlesha together.

Solution:

Efficiency of Isha: I = $$\frac{1}{24}$$​​

Efficiency of (Isha + Smriti):

I + S = $$\frac{1}{20}$$​​

So, efficiency of Smriti:

S =  $$\frac{1}{20} - \frac{1}{24}$$​​

= $$\frac{6 - 5}{120}$$​​

= $$\frac{1}{120}$$​​

Efficiency of (Isha + Smriti + Ashlesha):

I + S + A = $$\frac{1}{12}$$​​

So, efficiency of Ashlesha:

A = $$\frac{1}{12} - \frac{1}{20}$$​​

= $$\frac{5 - 3}{60}$$​​

= $$\frac{1}{30}$$​​

Now, efficiency of (Isha + Ashlesha):

I + A = $$\frac{1}{24} + \frac{1}{30}$$​​

= $$\frac{5 + 4}{120}$$​​

= $$\frac{9}{120}$$​​

= $$\frac{3}{40}$$​​

Time taken = $$\frac{40}{3}$$​ days

Alternate Solution(Exam- hall trick):