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 ($T_R$)
-
Equate the two expressions for Raju's time ($T_J$): $ \frac{T_R}{3} = T_R - 20 $
-
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 $
-
Rearrange the equation to group the terms with $T_R$ on one side: $ 60 = 3T_R - T_R $ $ 60 = 2T_R $
-
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
- 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?
- 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?
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?
- Five women can do a work in thirty six days. If the ratio between the capacity of a man and a woman is 3:1, then find how many days it will take 5 men to complete the same work?
- If 15 persons can do a job in 30 days, then 30 persons with twice the efficiency can do the same job in how many days?
- 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?
- John is only 40% as efficient as Jesse. If John alone can do a piece of work in 35 days, how many days will it take the duo to complete the work, if they work together?
- Kamal can complete a work in 14 days. Vimal is 40% more efficient than Kamal. The number of days Vimal will take to complete the same piece of work is:
- 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?
- 21 women can complete a task in 40 days. 30 men can complete the task in 21 days. What is the ratio of the number of days a man will take to complete the task alone to the number of days a woman will need to do that task?
Important Questions from Work Efficiency
Sumi can complete a job working 5 hours per day in 2 days. If she doubles her working hours per day, then in how many days will she complete the work?
Five men and 2 boys can do in 30 days as much work as 7 men and 10 boys can do in 15 days. How many boys should join 40 men to do the same work in 4 days?
A man completes 7/8 of a job in 21 days. How many more days will it take him to finish the job if quantum of work further increased by 50%?
24 men and 12 women can do a piece of work in 30 days. In how many days can 12 men and 24 women do the same piece of work?
3 men working 7 hours a day can complete a piece of work in 45 days. In how many days will 9 men working 6 hours a day complete the same work?
