# A is 50% more efficient than B. How much time will they take working together to complete a job, where B alone could have done in 20 days?

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A is 50% more efficient than B. How much time will they take working together to complete a job, where B alone could have done in 20 days?
1. 8
2. 40
3. 6
4. 12

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Correct Answer - Option 1 : 8

Given:

A is 50% more efficient than B.

Time taken by B alone = 20 days

Formula used:

Total work = Efficiency × Time

Where Efficiency is work done per day.

Calculation:

The efficiency of A = 150% of the efficiency of B

⇒ The efficiency of A = (3/2) of efficiency of B

⇒ (Efficiency of A)/(Efficiency of B) = 3/2

Now, Total efficiency of (A + B) = 3 + 2 = 5

We know that Time taken by B alone = 20 days.

So, Total work = (Efficiency of B) × (Time taken by B)

⇒ 2 × 20

⇒ 40

According to the question,

Time taken by (A + B) to complete the whole work = (Total work)/(Total efficiency)

⇒ 40/5

⇒ 8 days

∴ A and B both working together will complete the whole job in 8 days.