Anjani can do a certain piece of work in 30 days. Anjani and Khushbu can together do the same work in 24 days, and Anjani, Khushbu and Sushmita can do the same work together in 12 days. In how many days can Anjani and Sushmita do the same work?

Correct option is D

Given:

Anjani (A) alone = 30 days

Anjani + Khushbu (A+K) = 24 days

Anjani + Khushbu + Sushmita (A+K+S) = 12 days

Find time for Anjani + Sushmita (A+S)

Formula Used:

Rate =$$\frac 1{\text{Time}}$$​​

Time =$$\frac 1{\text{(combined rate)}}$$​​

Solution:

Rate of Anjali (A) = $$\frac 1{30}$$​​

Rate of Anjani + Khushbu (A+K) $$=\frac 1{24}$$​​

Rate of Anjani + Khushbu + Sushmita (A+K+S) = $$\frac 1{12}$$​​

K =$$\frac{1}{24} - \frac{1}{30} = \frac{1}{120}$$​​

S =$$\frac{1}{12} - \frac{1}{24} = \frac{1}{24}$$​​

A+S =$$\frac{1}{30} + \frac{1}{24} = \frac{9}{120} = \frac{3}{40}$$​ per day

Time =$$\dfrac{1}{\frac3{40}} = \dfrac{40}{3}$$​ days

Alternate Method:

Let total work = LCM(30, 24, 12) = 120 units

A $$= \frac {120}{30} =$$​ 4 units/day

A + K $$= \frac {120}{24}$$​ = 5

K = 1 unit/day

A + K + S =$$\frac {120}{12}$$​= 10

S = 10 - 5 = 5 units/day

A + S = 4 + 5 = 9 units/day

Time $$=\frac{ 120}9 = \frac{40}3$$​ days