Correct Answer - Option 3 : 48/7
Please note that the efficiency here is written as Sumit 5 times more than Rohit. In other words, In other words, the difference between the efficiency of Sumit and Rohit is 5.
Sumit : Rohit = 6 :1
In other questions, you will find statements like this " A is 5 times as efficient as B. so it means A is 500% and B is 100% or A : B = 5 : 1.
Given:
(Efficiency of Sumit)/(Efficiency of Rohit) = 6/1
No of days taken by Sumit = No. of days taken by Rohit to finish the work – 40 days
Concept:
The time taken by A and B to finish the work is reciprocal of their efficiency of doing work.
Calculation:
∵ (Efficiency of Sumit)/(Efficiency of Rohit) = 6/1
∴ Time taken by Sumit/Time taken by Rohit = 1/6
Let the time taken by Sumit = 1a
Time taken by Rohit = 6a
∵ No of days taken by Sumit = No. of days taken by rohit to finish the work – 40 days
⇒ 1a = 6a – 40
⇒ 6a – 1a = 40
⇒ 5a = 40
⇒ a = 40/5
⇒ a = 8
∴ Time taken by Rohit = 6 × 8 = 48 days
Time taken by Sumit = 1 × 8 = 8 days
∵ (Sumit + Rohit)’s 1 day’s work = (1/8) + (1/48)
= (6 + 1)/48
= 7/48
= 48/7
∴ Time taken by (Sumit + Rohit) to finish the work together = 48/7 days
⇒ 48/7 days