A can complete a task in the same time in which B and C together can complete it. If A and B together can complete it in 10 days and C alone can complete it in 60 days, then B alone can complete it in:

Correct option is D

Given:

A can complete a task in the same time in which B and C together can complete it.

A and B together can complete it in 10 days

C alone can complete it in 60 days

Formula used:

Total work = Work done each day (Efficiency) × Total time taken (in days)

Solution:

Let the entire work be the LCM of 10 and 60.

Hence, total work = LCM (10, 60) = 60 units

Efficiency of C = 60 ÷ 60 = 1 units

Let the efficiencies of A and B are P units and Q units a day respectively.

B and C together do each day = (Q + 1) units of work

According to the question,

60 ÷ P = 60 ÷ (Q + 1)

=> P = Q + 1      ....(1)

(P + Q) × 10 = 60

=> (P + Q) = 6

=> Q + 1 +  Q = 6

=> Q = 2.5

Hence, time taken by B to complete the work alone = 60 ÷ 2.5 = 24 days

∴ B will take 24 days to complete the work alone.