Rakesh can complete a piece of work in 6 hours, while Shivam can complete it…
2026
Rakesh can complete a piece of work in 6 hours, while Shivam can complete it in 14 hours. With Rupesh assisting them, all three complete the work in 3 hours. How many hours would Rupesh alone take to complete twice that amount of work?
Answer: C. 21 — ConceptFor work-rate problems, a worker who completes one job in t hours has rate 1/t job per hour. Rates add when people work together, and time equals…
- A.
20
- B.
22
- C.
21
- D.
23
Attempted by 24 students.
Show answer & explanation
Correct answer: C
Concept
For work-rate problems, a worker who completes one job in t hours has rate 1/t job per hour.
Rates add when people work together, and time equals required work divided by the relevant rate.
Application
Rakesh’s rate is 1/6 job per hour, and Shivam’s rate is 1/14 job per hour.
Their combined rate is 1/6 + 1/14 = 7/42 + 3/42 = 10/42 = 5/21 job per hour.
The three workers together finish one job in 3 hours, so their combined rate is 1/3 = 7/21 job per hour.
Therefore Rupesh’s rate is 7/21 − 5/21 = 2/21 job per hour.
For twice the work, the required amount is 2 jobs. Hence the time is 2 ÷ (2/21) = 2 × 21/2 = 21 hours.
Cross-check
In 21 hours, Rupesh completes 21 × (2/21) = 2 jobs, exactly twice the original work. Therefore, Rupesh alone takes 21 hours.