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21 Apr 2022, 06:30
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65% (01:51) correct
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To complete a piece of work alone, Rakesh takes two – third of the time that Rajesh takes to complete alone. If they together complete the same work in 2.4 days, how long would Rakesh take to complete it alone?
(A) 4 days
(B) 6 days
(C) 9 days
(D) 10 days
(E) 11 days
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
(A) 4 days
(B) 6 days
(C) 9 days
(D) 10 days
(E) 11 days
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
05 May 2022, 21:25
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From the question, Rakesh takes two-thirds of the time that Rajesh takes to complete alone.
i.e., the time taken to complete a piece of work by Rakesh and Rajesh is in the ratio of 2 : 3.
Let us take the time taken by Rakesh and Rajesh to be 2x and 3x.
Given Rakesh takes 2x days to complete a work, the fraction of work completed by Rakesh alone in 1 day is \(\frac{1}{2x}\).
Similarly, Rajesh takes 3x days to complete a work, the fraction of work completed by Rajesh alone in 1 day is \(\frac{1}{3x}\).
When Rakesh and Rajesh work together, they complete the work in 2.4 days. Then, the fraction of work completed by Rakesh and Rajesh working together in 1 day is \(\frac{1}{2.4}\).
Given Rakesh and Rajesh are working together, the fraction of work completed by them in one day will be equal to the sum of the fraction of work completed by Rakesh working alone and the fraction of work completed by Rajesh working alone.
Equating them we get,
\(\frac{1}{2x}\) + \(\frac{1}{3x}\) = \(\frac{1}{2.4}\)
\(\frac{5}{6x}\) = \(\frac{1}{2.4}\)
\(\frac{5}{6} * 2.4\) = x
x = 2
2x = 4 days & 3x = 6 days
Then Rakesh and Rajesh takes 4 and 6 days respectively to complete the task.
The answer is Choice (A) 4 days.
i.e., the time taken to complete a piece of work by Rakesh and Rajesh is in the ratio of 2 : 3.
Let us take the time taken by Rakesh and Rajesh to be 2x and 3x.
Given Rakesh takes 2x days to complete a work, the fraction of work completed by Rakesh alone in 1 day is \(\frac{1}{2x}\).
Similarly, Rajesh takes 3x days to complete a work, the fraction of work completed by Rajesh alone in 1 day is \(\frac{1}{3x}\).
When Rakesh and Rajesh work together, they complete the work in 2.4 days. Then, the fraction of work completed by Rakesh and Rajesh working together in 1 day is \(\frac{1}{2.4}\).
Given Rakesh and Rajesh are working together, the fraction of work completed by them in one day will be equal to the sum of the fraction of work completed by Rakesh working alone and the fraction of work completed by Rajesh working alone.
Equating them we get,
\(\frac{1}{2x}\) + \(\frac{1}{3x}\) = \(\frac{1}{2.4}\)
\(\frac{5}{6x}\) = \(\frac{1}{2.4}\)
\(\frac{5}{6} * 2.4\) = x
x = 2
2x = 4 days & 3x = 6 days
Then Rakesh and Rajesh takes 4 and 6 days respectively to complete the task.
The answer is Choice (A) 4 days.
06 May 2022, 06:49
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Time taken by Rakesh = \(\frac{2}{3}\) (Time taken by Rajesh)
Therefore, Rate of Rakesh = \(\frac{3}{2}\) (Rate of Rajesh)
Or, Rate of Rakesh / Rate of Rajesh = \(\frac{3 }{ 2}\)
Let rate of Rakesh = 3 units per day and rate of Rajesh = 2 units per day
If they work together, combined rate = 5 units per day.
It is given that they completed the work in 2.4 days. Therefore, total work = 5 * 2.4 = 12 units.
Time taken by Rakesh to complete the work alone = \(\frac{12 }{ 3}\) = 4 days
The correct answer option is A.
Therefore, Rate of Rakesh = \(\frac{3}{2}\) (Rate of Rajesh)
Or, Rate of Rakesh / Rate of Rajesh = \(\frac{3 }{ 2}\)
Let rate of Rakesh = 3 units per day and rate of Rajesh = 2 units per day
If they work together, combined rate = 5 units per day.
It is given that they completed the work in 2.4 days. Therefore, total work = 5 * 2.4 = 12 units.
Time taken by Rakesh to complete the work alone = \(\frac{12 }{ 3}\) = 4 days
The correct answer option is A.
