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.
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Important Questions from Work Efficiency
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A and B together can do a piece of work in 4 days, B and C can do it in 6 days, A and C can do it in 8 days. Then A, B and C together can do the same work in :-
A can complete 50% of a work in 9 days and B can do 25% of the work in 9 days, if they work alone. If they work together then how much work (in percentage) can be completed in 6 days?
A is thrice as good a workman as B. C alone takes 48 days to paint a house. All three A, B and C working together take 16 days to paint the house. It will take how many days for A alone to paint the house?
