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Sumit is five times more efficient than Rohit and can finish a work in 40 days less than Rohit. In what time they together can finish the work?
1. \(5{1\over 2}\)
2. \(7{2\over 3}\)
3. 48/7
4. \(3{1 \over 5}\)

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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

 

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