Rohit and mohit can complete a piece of work in 5 days. Time taken by mohit alone to complete the same work is 7.5 days more than the time taken by rohit alone to complete the same work. In how many days rohit alone will complete two-third of the work?
Answers
Step-by-step explanation:
- Rohit and mohit can complete a piece of work in 5 days
R + M = 5 days
- Time taken by mohit alone to complete the same work is 7.5 days more than the time taken by rohit alone to complete the same work
capacity= work/time
we can equate for time ,
T = W/C,
7.5 = 15/M - 15/ R
assume R and M,
M = 1
R = 2 ,because of taking 7.5 days less,his capacity is more.
In how many days rohit alone will complete two-third of the work
15*2/3 = 10
R = 10/2 = 5 days
To complete two-thirds of the work, Rohit will need 5 days
Given:
Rohit and Mohit can complete a piece of work in 5 days. The time taken by Mohit alone to complete the same work is 7.5 days more than the time taken by Rohit alone to complete the same work.
To find:
In how many days rohit alone will complete two-thirds of the work?
Solution:
Let's assume that Rohit can complete the work alone in 'x' days.
The work can be done by Rohit = 1/x
Mohit can complete the same work alone in 'x + 7.5' days
The work done by Mohit in one day = 1/(x + 7.5)
Rohit and Mohit can complete the work together in 5 days.
=> 5 [1/x + 1/(x + 7.5)] = 1
=> 5 [ x + 7.5 + x ]/ x(x + 7.5) = 1
=> 10x + 37.5] = x(x + 7.5)
=> 10x + 37.5 = x² + 7.5x
=> x² + 7.5x - 10x - 37.5 = 0
=> x² - 2.5x - 37.5 = 0
Solving this quadratic equation, we get:
x = 7.5 or R = - 5
Since x cannot be negative, we can take x = 7.5
Therefore, Rohit can complete the work alone in 7.5 days, and Mohit can complete the same work alone in 15 days (since x + 7.5 = 13.5).
The work done in 1 day by Rohit = 1/7.5
Let Rohit can complete two-thirds of the work in 'y' days
=> 1/7.5 (y) = 2/3
=> y = 2(7.5)/3
=> y = 15/3
=> y = 5
Therefore,
To complete two-thirds of the work, Rohit will need 5 days
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