The ratio of the efficiencies of A and C is 2 : 5 and the ratio of the efficiencies of B and D is 1 : 2. If B alone takes 12 more days than A alone to complete the work and D alone takes 8 more days than C alone to complete the work, then in how many days they together can complete the work?

The ratio of the efficiencies of A and C is 2 : 5 and the ratio of the efficiencies of B and D is 1 : 2. If B alone takes 12 more days than A alone to complete the work and D alone takes 8 more days than C alone to complete the work, then in how many days they together can complete the work? Correct Answer 3(31/43) days

Let the time taken by A alone and B alone to complete the work be ‘x’ days and ‘y’ days respectively.

So, the time taken by C alone to complete the work = x × 2/5 = (2x/5) days

And the time taken by D alone to complete the work = y × 1/2 = (y/2) days

From the question:

y – x = 12

y = x + 12   ---- (1)

And, (y/2) – (2x/5) = 8   ---- (2)

From equations (1) and (2):

– = 8

(5x + 60 – 4x)/10 = 8

x + 60 = 80

x = 20 and y = 32

The time taken by A alone and B alone to complete the work is 20 days and 32 days respectively.

The time taken by C alone to complete the work = 20 × 2/5 = 8 days

The time taken by D alone to complete the work = 32/2 = 16 days

Now, (1/A) + (1/B) + (1/C) + 91/D) = (1/20) + (1/32) + (1/8) + (1/16) = 43/160