Work Time Calculation: Raju and Ravi Problem
This problem involves comparing the work efficiency and time taken by two individuals, Raju and Ravi.
Problem Setup
Let the time taken by Ravi to complete the piece of work be $T_R$ days.
Let the time taken by Raju to complete the same work be $T_J$ days.
We are given that Raju is thrice as good a workman as Ravi. This means Raju's work rate is 3 times Ravi's work rate.
When one person's work rate is higher, they take less time to complete the same amount of work. Specifically, if Raju's rate is 3 times Ravi's, Raju's time will be 1/3 of Ravi's time.
Therefore, the relationship between their times is: $T_J = \frac{T_R}{3}$
We are also given that Raju takes 20 days less than Ravi to complete the work. This can be written as: $T_J = T_R - 20$
Solving for Ravi's Time ($T_R$)
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Equate the two expressions for Raju's time ($T_J$): $ \frac{T_R}{3} = T_R - 20 $
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To eliminate the fraction, multiply both sides of the equation by 3: $ 3 \times \frac{T_R}{3} = 3 \times (T_R - 20) $ $ T_R = 3T_R - 60 $
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Rearrange the equation to group the terms with $T_R$ on one side: $ 60 = 3T_R - T_R $ $ 60 = 2T_R $
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Solve for $T_R$ by dividing by 2: $ T_R = \frac{60}{2} $ $ T_R = 30 $
So, the time taken by Ravi to complete the work is 30 days.
Similar Questions
- Raju is thrice as good as a workman as Vinod and together they can finish a task in 21 days. In how many days can Vinod alone complete the work?
- A can do $\frac{1}{5}^{\text{th}}$ of some work in 12 days, B can do $20\%$ of the same work in 10 days, C can do $\frac{1}{6}^{\text{th}}$ of the work in 8 days and D can do $\frac{1}{5}^{\text{th}}$ of the work in 12 days. Who will complete the work first if all four started to work at the same time?
- Raj is 60% more efficient than Sundar and Sundar can finish a certain task in 16 days. How many days will Raj alone take to complete the same task?
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- A can do a certain work in 45 days. B is 50% more efficient than A, and C is 3 times as fast as A. They started the work together but C left 7 days before completion of the work. In how many days was the entire work completed?
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Manoj is twice as efficient a fisherman as Anuraj, and together they complete a piece of work in 22 days. In how many days can Anuraj alone complete the same work?
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Important Questions from Work Efficiency
A and B together can complete a certain work in 20 days whereas B and C together can complete it in 24 days. If A is twice as good a workman as C, then in what time will B alone do 40% of the same work?
14 men can complete a work in 15 days. If 21 men are employed, then in how many days will they complete the same work?
A can do a certain work in 15 days, while B can do the same work in 21 days. If they work together, then in how many days will the same work be completed?
To do a certain work, A and B work on alternate days with B beginning the work on the first day. A alone can complete the same work in 24 days. If the work gets completed in \(11 \frac{1}{3}\) days, then B alone can complete \(\rm \frac{7}{9}^{th}\) part of the original work in:
Two men and 7 women can complete a work in 28 days whereas 6 men and 16 women can do the same work in 11 days. In how many days can 7 men complete the same work?
