One day, Rahul started a work at 9 AM and Gautam

Question

One day, Rahul started a work at 9 AM and Gautam joined him two hours later. They then worked together and completed the work at 5 PM the same day. If both had started at 9 AM and worked together, the work would have been completed 30 minutes earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is

A. 10
B. 10.5
C. 11
D. 11.5
E. 12

Source : Wzako

Show Answer

Official Answer

A

A. 10
B. 10.5
C. 11
D. 11.5
E. 12

Source : Wzako

Solenja · Answer

Let Rahul work at a units/hr and Gautam at b units/hour
Now as per the condition : 8a+6b =7.5a+7.5b 
so we get 0.5a=1.5b or a=3b
Therefore total work = 8a +6b = 8a +2a =10a
Now Rahul alone takes 10a/10...
(Source:internet)

Suruchim12 · Answer

Bunuel  Hi, Could you please help provide an explanation to this question.

TIA

Bunuel · Answer

One day, Rahul started a work at 9 AM and Gautam joined him two hours later. They then worked together and completed the work at 5 PM the same day. If both had started at 9 AM and worked together, the work would have been completed 30 minutes earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is

A. 10
B. 10.5
C. 11
D. 11.5
E. 12

Source : Wzako

Show Answer

Official Answer

A

A. 10
B. 10.5
C. 11
D. 11.5
E. 12

The stem gives two scenarios of how the job can be done:

1. Rahul works for 2 hours alone + Rahul and Gautam work for 6 hours together.

2. Rahul and Gautam work for 7.5 hours together.

So,  Rahul and Gautam working for 1.5 hours together = Rahul working for 2 hours alone :

1.5(x + y) = 2x, where x is the rate of Rahul and y is the rate of Gautam. This gives x = 3y (Rahul is 3 times as efficient as Gautam).

Now, the total work equals to 2x + 6(x + y) = 8x + 6y = 8x + 6*x/3 = 10x. Therefore, time Rahul would have taken, in hours, to complete the work is time = work/rate = 10x/x = 10 hours.

Answer: A.

Rabab36 · Answer

how you calculated

he stem gives two scenarios of how the job can be done:

1. Rahul works for 2 hours alone + Rahul and Gautam work for 6 hours together.

2. Rahul and Gautam work for 7.5 hours together.

sir pls elaborate

stne · Answer

Dear  Rabab36 ,

Let me try:

Let Rahul be able to complete the work alone in  x  and Gautam alone in  y  hours.

So in two hours Rahul would complete  \frac{2}{x}

Remaining work =   1- \frac{2}{x}  =  \frac{x-2}{x}

Now this remaining work was completed together in  6  hours by both Rahul and Gautam

\frac{6}{x}+ \frac{6}{y} = \frac{x-2}{x}

\frac{1}{x}+ \frac{1}{y} = \frac{x-2}{6x} ...(I)

If they had worked together from 9:00am to 4:30pm then work would have been completed in  7.5  hrs

\frac{1}{x} + \frac{1}{y}= \frac{1}{7.5} ...(II)

(I) - (II)

\frac{x-2}{6x}- \frac{1}{7.5}=0

7.5x -15 -6x = 0

1.5x= 15

x= \frac{150}{15} =10

Ans A

Hope it's clear.

Nielgmat · Answer

1. Let Rahul take 'R' hours to complete the job alone, and Gautam take 'G' hours to complete the job alone.
2. So in Rahul will complete 1/R of the work in 1 hour, Gautam will complete 1/G of the work in 1 hour. (Rates of work in either cases)
3. Since Rahul works alone for 2 hours and Rahul & Gautam work together for 6 hours, the eqn can be written as under:-
 (1/R) x2 + (1/R + 1/G) x6 = 1 (1 = one full work) ..........Eqn 1
 Simplifying the above , you will get,
 G = 3R....Eqn 1a

4. Now next day both work together from 9 am and finish the job 30 mins earlier ..i.e. in 7.5 hrs
 So the Eqn can be written as under:-
   x 7.5 = 1............Eqn 2

substituting G = 3R in Eqn 2
 (1/R + 1/3R ) x 7.5 = 1
 solving the above should give you R = 10

5. R was the time taken by Rahul to do the job alone

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One day, Rahul started a work at 9 AM and Gautam

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