Correct Answer - Option 4 : 40/3 days
Given:
A = 50% more efficient than B
C = 1/2 of work done by A and B together
C alone can do the work in = 40 days
Calculation:
(A’s one day’s work) : (B’s one day’s work)
⇒ 150 : 100
⇒ 3 : 2
Let A’s one day’s work be 3x and B’s one day’s work be 2x.
∴ According to the question
C’s one day’s work = (3x + 2x)/2
⇒ 5x/2 = 1/40
⇒ x = (1/40) × 2/5
⇒ x = 1/100
A’s one day’s work be 3/100 and B’s one day’s work be 1/50.
∴ (A + B + C)’s one day’s work:
⇒ 3/100 + 1/50 + 1/40
⇒ 15/200
⇒ 3/40 = (A + B + C)'s one day work
A, B, C can complete the whole work in 40/3 days.
∴ A, B, and C can complete the work in 40/3 days.