A alone can do a task in 39 days, whereas B alone can do it in 52 days. The duo start working together, but A leaves 3 days before the task gets over. For how many days did the two work together?

Correct option is D

Given:

A can do a task in 39 days.

B can do the same task in 52 days.

A and B work together, but A leaves 3 days before the task is completed.

Formula Used :

Work = Efficiency × Time

Solution:

Let the total work be W.

LCM(39, 52) = 156. So, let W = 156 units.

Efficiency of A = $$\frac{\text{Work}}{\text{Time}} = \frac{156}{39}$$​ = 4 units/day

Efficiency of B =$$\frac{\text{Work}}{\text{Time}} = \frac{156}{52}$$​= 3 units/day

Let 'x' be the number of days A and B worked together.

B worked for a total of x + 3 days, as A left 3 days before the work was completed.

Total work done:

(Work done by A and B together) + (Work done by B alone)= Total Work

(A's efficiency + B's efficiency)$$\times$$x + (B's efficiency)$$\times$$ 3= 156

(4 + 3) x + 3 $$\times$$ 3= 156

7x + 9 = 156

7x = 156 - 9

7x = 147

x = 21

Therefore, A and B worked together for 21 days.