Question

Harry claims to complete an assignment in 24 days while Ron claims to finish the same in 36 days. They decided to work together on alternative days starting with Harry. In how many days  assignment will be completed.
1. 12(1/2)
2. 37(1/2)
3. 28(2/3)
4. 50
5. 30

Answer 1

Correct Answer - Option 3 : 28(2/3)

Given 

Harry completes an assignment in = 24 days

Ron completes same assignment in = 36 days 

They work alternatively on the same assignment 

Concept used

Work = time × efficiency 

Calculation 

LCM of 24 and 36 = 72 i.e. total work = 72 units 

Efficiency of Harry = 3 units / per day 

Efficiency of Ron = 2 units / per day 

2 days efficiency of  Harry and Ron when they decided to work alternative days = 3 + 2 = 5 units

In (2 × 14) days the work done = 5 × 14 = 70

Remaining work = 2

On the 29^th day, it's Harry's turn, required time = 2/3 days

Total work will be completed by both in = 28(2/3) days

∴ 28(2/3) days are required to complete the work.