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07 Aug 2024, 13:45
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
44% (03:56) correct
56%
(02:43)
wrong
based on 45
sessions
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Ram and Shyam can complete a work together in 24 days. Ram is 50 percent more efficient than Shyam. They started working and Ram took rest every 2nd day and Shyam every 3rd day. On which day will the work get completed?
A. 48
B. 47
C. 45
D. 43
E. 41
A. 48
B. 47
C. 45
D. 43
E. 41
07 Aug 2024, 14:07
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Bunuel
This is a very tricky question
I took total work as 120. That means they can work in 24 days
Ram 1.5x
Shyam x
Total 2.5x unit/ day
This was we can get x=2
so together they can work
Ram 3 unit per day
Shyam 2 unit per day
Now
Ram took rest every 2nd day and Shyam every 3rd day. So 1st day they must have worked together- 5 units done
left- 115 units
every 2nd and 3rd day they can do 5 unit work
so that way 115 units can be completed in
5 units- 2 days
115 units - 2/5*115= 46 days
Dont forget to count the first day
So the answer would be 46+1= 47 days
B
07 Aug 2024, 22:25
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Method 1: Efficiency
Ram and Shyam can complete a work (working togther) in \(24\) days. And Ram is \(50\%\) more efficient than Shyam, i.e. \(\dfrac{R}{S} = \dfrac{15}{10} = \dfrac{3}{2}\).
Thus, the effeciency of Ram and Shyam was already given in the problem statement and equation the above would result in \(R = 3\), and \(S = 2\).
Working together they completed the work in 24 days. Therefore, \(\text{total amount of work} = \text{Total efficiency} \times \text{Time to complete the work(in days)} = (R+S) \times 24 = (3+2) \times 24 = 120\).
Now the problem statement state that every \(2^{nd}\) and \(3^{rd}\) day Ram and Shyam takes rest. Thus, the pattern is \((R+S), S, R, S, R, \dots \).
Therefore, on \(1^{st}\) day, they worked together, efficiency \(= (R+S) = 5\). Amount of work done on the \(1^{st}\) day \(= 120 - 5 = 115\) remaining.
The remaining work of \(115\) was completed by Ram and Shyam on alternative days. Or, on \(2^{nd}\) day shyam complete \(2\) amount of work and on \(3^{rd}\) day Ram completes \(3\) amount of work which is \(5\) amount of work in \(2\) days.
Thus, the time taken to complete the work \(= 1 + 115 \times \dfrac{2}{5} = 1 + 46 = 47\) days.
B
If you don't understand, then REPEAT! An upvote (+1) would be appreciated
Ram and Shyam can complete a work (working togther) in \(24\) days. And Ram is \(50\%\) more efficient than Shyam, i.e. \(\dfrac{R}{S} = \dfrac{15}{10} = \dfrac{3}{2}\).
Thus, the effeciency of Ram and Shyam was already given in the problem statement and equation the above would result in \(R = 3\), and \(S = 2\).
Working together they completed the work in 24 days. Therefore, \(\text{total amount of work} = \text{Total efficiency} \times \text{Time to complete the work(in days)} = (R+S) \times 24 = (3+2) \times 24 = 120\).
Now the problem statement state that every \(2^{nd}\) and \(3^{rd}\) day Ram and Shyam takes rest. Thus, the pattern is \((R+S), S, R, S, R, \dots \).
Therefore, on \(1^{st}\) day, they worked together, efficiency \(= (R+S) = 5\). Amount of work done on the \(1^{st}\) day \(= 120 - 5 = 115\) remaining.
The remaining work of \(115\) was completed by Ram and Shyam on alternative days. Or, on \(2^{nd}\) day shyam complete \(2\) amount of work and on \(3^{rd}\) day Ram completes \(3\) amount of work which is \(5\) amount of work in \(2\) days.
Thus, the time taken to complete the work \(= 1 + 115 \times \dfrac{2}{5} = 1 + 46 = 47\) days.
B
If you don't understand, then REPEAT! An upvote (+1) would be appreciated
