Question

Ravinder can cut a tree in 6 days, Sudhir can cut the same tree in 12 days and Sunder can cut it in 18 days. Ram is thrice as efficient as Sunder. If Ravinder worked on the same tree for 1 days, Sudhir worked for 2 days and Sunder worked for 3 days. Find the number of days Ram will take to cut the remaining tree alone.

1. 3 days 
2. 4 days
3. 2 days 
4. 1 day
5. None of these

Answer 1

Correct Answer - Option 1 : 3 days 

Given

Ravinder, Sudhir and Sunder can cut a tree respectively = 6 days, 12 days and 18 days

Efficiency of Ram then Sunder = Thrice

Formula Used

Work = Time × Efficiency

Calculation

Worked done by Ravinder in 1 day = 1/6

Worked done by Sudhir in 1 day = 1/12

Worked done by Sunder in 1 day = 1/18

Since Ram is trice as efficient as Sunder,

So work done by Ram in 1 day = (1/18) × 3 = 1/6

Remaining work = 1 – 1/6 – 2/12 – 3/18

⇒ = 1/2

Let the time taken by Ram to complete the remaining work alone = x days

According to question

⇒ x/6 = 1/2

⇒ x = 6/2 = 3 day

∴ Time taken by Ram to complete the remaining work alone is 3 day.