# A is 50% more efficient as B. C can do half of the work done by A and B together. If C alone can do the work in 40 days, then A, B, and C together can

39 views
in Aptitude
closed
A is 50% more efficient as B. C can do half of the work done by A and B together. If C alone can do the work in 40 days, then A, B, and C together can do the work in how many days?
1. 44/3 days
2. 43/3 days
3. 41/3 days
4. 40/3 days
5. 50/3 days

by (54.3k points)
selected

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.