If A and B work together, they will complete a job in 7.5 days. Howeve

Question

If A and B work together, they will complete a job in 7.5 days. However, if A works alone and completes half the job and then B takes over and completes the remaining half alone, they will be able to complete the job in 20 days. How long will B alone take to do the job if A is more efficient than B?

(A) 20 days
(B) 24 days
(C) 30 days
(D) 35 days
(E) 40 days

(A) 20 days 
(B) 24 days 
(C) 30 days 
(D) 35 days
(E) 40 days

EgmatQuantExpert · Accepted Answer

Solution 
  Given:  
 • A and B working together will complete a job in 7.5 days
• A works alone for few days and completes half the job
• After that, B takes over and completes the remaining half of the job, working alone
• Total time taken to complete the job = 20 days
• A is more efficient than B

To find:  
 • The time taken by B alone to complete the entire job

Approach and Working:   
 • A + B one day’s work =  \frac{1}{7.5} = \frac{2}{15}

Let us assume that A works for x days to complete half the job
 • Implies, A’s one day work =  \frac{1}{2x}

This implies, B takes 20 – x days to complete the remaining half of the work
 • Implies, B’s one day work =  \frac{1}{(2*(20 – x))}

Thus,  \frac{1}{2x} + \frac{1}{(2*(20 – x))} = \frac{2}{15} 
 • Implies,  \frac{1}{x} + \frac{1}{(20 – x)} = \frac{4}{15}

Simplifying this, we get,
 • x * (20 – x) = 5 * 15

Comparing the terms on both sides, we can infer that x = 5
 • Thus, B’s one day work =  \frac{1}{(2*15)} = \frac{1}{30}

Therefore, B alone takes 30 days to complete the entire job

Hence, the correct answer is Option C

Answer: C

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effatara · Answer

In this problem, any algebraic solution would involve a quadratic equation, factorization etc hence time-consuming. Using the answer choices is a much quicker option:
Let 'x' and 'y' be the number of days needed by A and B respectively to do the job alone. Then A does half the job in x/2 days and B the remaining half in y/2 days. (x/2+y/2)=20...> x+y=40.....(i)
Working together, A and B can finish the job in 7.5 days. Therefore:
7.5 (1/x + 1/y) = 1...> {7.5(x+y)/xy}=1...> 7.5*40=xy...> xy=300.....(ii)
Answer Option (A): If 'y' (days needed by B to do the job alone) is 20 'x' is also 20, xy=400 so NO.
Option (B): If 'y' is 24 'x' is 16, xy=384. NO
(C): y=30, x=10. YES. ANS:C

AdityaHongunti · Answer

chetan2u  i tried to use the options but i cannot undertsnad what to do in case where we have to find the less effecient ..
i used your stsrategy to get a range for more sufficient one but how to do this quickly when we are asked for less effeicient one coz i:m not able to come up with a range for less effeicinet. is there any other starategy where i use answer choices???

indugopal1991 · Answer

A and B together can complete the job in 7.5 days. If A do half of the jobs then B do half of the jobs they can complete in 20 days.

If we take multiplication of 7.5 and 20 = 150 as total work.

Then combine work in one day is = 150/7.5=20, A is more efficient than B, so if we consider A is doing 15 while B is doing 5(randomly easy to work, ball parking).

so total job we have considered = 150, half the job = 75.

A do half the job in 75/15 = 5 days
B do half of the jobs in 75/5 = 15 days.

Which satisfy with the statement that, after half done by A, B do half and complete in 20 days.

So B can do the entire job in 150/5 = 30 days

Anu5162 · Answer

Solving through options
Starting with the middle one. Lets assume B alone takes 30 days. Then it would take B 15 days to finish half the work. So first half must have been already done by A in 5 days (since they take 20 days to finish half thw work one by one)

Now using this information to verify the data when they work together. Working alone A should take (5×2) 10 days. And we know B takes 30 days (assumption)
At this rate working together they should take 7.5 days. (Matches with the info given to us)

Hence option C

If you have time you can also sww why other options are wrong
 
A. Assuming B takes 20 days. Half work = 10 days. This means first half for A is also 10 (not possible since A is more efficient)
B. Assuming B takes 24 days. Half work = 12 days. Half work for A is then 8 days. That means A shud take 16 days to complete. Together they wont be taking 7.5 days

And so on

Posted from my mobile device

gracie · Answer

note that only option C is a multiple of 7.5
rate of A+B working together=1/(7.5)=4/30
if A is more efficient than B, 
then A's rate=3/30 and B's rate=1/30
1/30+3/30=4/30
30 days
C

Baps · Answer

Hi Team,

Quick question on my side.

When I tried to resolve this problem, I did the following :

First information given : 1/A + 1/B = 7.5 = 2/15

Second information given 1/2A + 1/B = 1/20

Then, First information - Second information = 1/A - 1/2A + 1/B - 1/B = 2/15 - 1/20. That gave me A = 6.

Therefore, 1/6 + 1/B = 2/15, meaning 1/B = -1/30. I knew that "B" couldn't be <0 but I still picked "C" as an answer because the denominator was equal to 30.
Can someone explain to me what did I do wrong

I just can't get my head around it.
Thanks !

I just can't get my head around it. Thanks !

KarishmaB · Answer

Take a cue from the options.

If A and B work together, they will complete a job in 7.5 days. However, if A works alone and completes half the job and then B takes over and completes the remaining half alone, they will be able to complete the job in 20 days. How long will B alone take to do the job if A is more efficient than B?

(A) 20 days
(B) 24 days
(C) 30 days
(D) 35 days
(E) 40 days

Each does half the work one after the other and they take 20 days. So B is much slower than A that is why 5 extra days were taken. So of the 20 days, B certainly took more than 10 days to complete his half. Hence B alone will certainly take much more than 20 days for the work. 
But B could not have taken 40 days alone either because then he would need 20 days for half the work alone but in 20 days, A also worked.

Hence 30 days for B alone seems reasonable. B could have done half the work in 15 days which means that A took the leftover 5 days for half the work. So A takes 10 days for full work.

Check: 1/10 + 1/30 = 2/15 = 1/7.5
So rate of work of A and B together is 1/7.5 which means they will take 7.5 days to complete the work together. This works.

Answer (C)

If A and B work together, they will complete a job in 7.5 days. Howeve

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If A and B work together, they will complete a job in 7.5 days. Howeve

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