If A and B can finish a work in 10 days, B and C can finish the same work in 12 days, C and A can finish the same work in 15 days; then in how many days can A, B and C together finish half of the work?

Given:

A and B can finish a work = 10 days

B and C can finish a work = 12 days

C and A can finish a work = 15 days

Concept Used:

Time taken = total work/efficiency to complete work

LCM of (10, 12,15) = 60

Calculation:

According to question

1/A + 1/B = 1/10         --------(1)

1/B + 1/C = 1/12        ---------(2)

1/C + 1/A = 1/15        ---------(3)

Adding equations (1),(2) & (3)

2(1/A + 1/B + 1/C) = 1/10 + 1/12 + 1/15

2(1/A + 1/B + 1/C) = (6 + 5 + 4)/60 = 15/60 = 1/4

(1/A + 1/B + 1/C) = 1/8

Efficiency to complete work of A,B & C = 8 days

A, B, and C together finish half of the work = 8/2 = 4 days

∴ The correct answer is 4 days.

Shortcut TrickTotal work = LCM of (10, 12,15) = 60

Efficiency of A + B = 60/10 = 6

Efficiency of B + C = 60/12 = 5

Efficiency of A + C = 60/15 = 4

Efficiency of 2 (A + B + C) = 6 + 5 + 4 = 15

Efficiency of A + B + C = 15/2 = 7.5

Time taken by A + B + C to complete half work = Half work/Efficiency

⇒ 30/7.5 = 4 days

∴ The correct answer is 4 days.