Working alone, B takes 12 more days than A to finish a certain job. B

Question

Working alone, B takes 12 more days than A to finish a certain job. B and A start working on the job together but A stops working 12 days before the job is done. B completes 60% of the job. In how many days can B do the job if working alone ?

A. 48 days
B. 36 days
C. 32 days
D. 30 days
E. 28 days

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Official Answer

B

A. 48 days
B. 36 days
C. 32 days
D. 30 days
E. 28 days

Are You Up For the Challenge: 700 Level Questions

eakabuah · Accepted Answer

Let time taken by A to finish the work be  x  days. Then B takes  x+12  days.
We are given that A stops working 12 days to the completion period when both start working on the same day.
Let t be the total time taken to complete the work.
Then
 \frac{t}{x+12}+\frac{t-12}{x}=1 ------(1) 
Also we are given that B did 60% of the work hence  \frac{t}{x+12}=\frac{3}{5}  
 5t=3x+36 ------(2) 
Likewise we can infer that A did 40% of the work, hence  \frac{t-12}{x}=\frac{2}{5} 
 5t=2x+60 -----(3) 
 (2)-(3)  ===>  x=24 
Time taken by B  =x+12=36

The answer is B.

sambitspm · Answer

Given B = 12+ A days to complete job
Say n are the days to complete the job

so (n/ A + n/B) + 12/B =1

Also it is given that B completed 60% work so (n+12)/B = 0.6
=> n = 0.6B -12

From our initial equation we get n / A = 0.4
n = 0.4 A
n = 0.4 B + 0.4*12

Solving n, we get B as 36

effatara · Answer

Let x days be the time taken B to complete the job and y days the time they work together.

Fraction of work done by B: y/x + 12/x = 3/5 (since it is given that B does 60% of the total work)
T/4, 3x=5y+60...........(i)
Fraction of the work done by A: y/(x-12)=2/5...> 2x=5y+24..........(ii)

Subtracting (ii) from (i), we get x=36. ANS: B

GMATWhizTeam · Answer

Solution 
 • Let assume that total 1 unit of work is involved in finishing the job and working alone B can finish the job in t days.
 o So, working alone A can finish the Job in t – 12 days. 
• Also, let us assume that A and B together worked for x days.
• Based on the above assumption and the information given in the question, let’s make the below table:
 https://www.dropbox.com/s/lk1oporjyn7b6q2/31_07_work.jpg?dl=1 
• Now, B finishes 60% of the job.
 o This means,  \frac{x}{t} + \frac{12}{t} =\frac{3}{5} 
o  ⟹ 5*(x+12) = 3t ⟹ 5x = 3t - 60 ….Eq.(i)  
• And A finishes 40% of the job.
 o So,   \frac{x}{t-12} = \frac{2}{5}  
o   ⟹5x = 2t -24  
• Now, substituting the value of 5x into Eq.(i), we get,
 o  2t – 24 = 3t – 60 ⟹ t = 36   
Thus, the correct answer is  Option B.

TestPrepUnlimited · Answer

Set the efficiencies for A and B as  a  and  b . We are given 
 \frac{1}{b} = \frac{1}{a} + 12 
 b * x + a(x - 12) = 1  where x is the amount of days it took b in this process. 
 b*x = 0.6

Eliminate x first, the second equation would be  0.6 + a(\frac{0.6}{b} - 12) = 1 .
We have  \frac{1}{b} = \frac{1}{a} + 12  so we can replace 1/b too.

Finally  0.6 + a*(\frac{0.6}{a} + 7.2 - 12) = 1 
 \frac{0.6}{a} - 4.8 = \frac{0.4}{a} 
 \frac{0.2}{a} = 4.8 
 \frac{1}{a} = 4.8/0.2 = 24 . Then 1/b = 24 + 12 = 36.

Ans: B

bhupendersingh27 · Answer

Let total no of days for B = x days
total no of days for A = y days

As B alone take 12 days:- x-y = 12 .... eq-1

work done by B: 60%, therefore time taken by B: 0.6x
work done by A: 40%, therefore time take by A: 0.4y

A stopped working 12 days before B:- 0.6x-0.4y=12.......eq-2

Multiply eq-1 by 0.4 and solve eq-1 & eq-2

0.4x - 0.4y = 4.8
0.6x - 0.4y = 12

0.2x = 7.2
x = 36 days

I find this method simple with less calculation. 
Experts please advice whether I can use this method in other similar questions.

AnkithaSrinivas · Answer

chetan2u  if we pick answers, say B 
 Bunuel 
if B takes 36 days to complete 100% of job

then it should satisfy that B should take 12 days to complete 60% of job. is my reasoning correct? please help

chetan2u · Answer

It may not be correct.

B takes 36 days to finish work, then he will take 36*60/100 or 21.6 days to finish 60% of work.

AnkithaSrinivas · Answer

but the answer should have been in such a way that we get 12 days, correct?

chetan2u · Answer

Two more ways other than the ones shown above.

(I) Options

If you were to choose options to do the work.

Say we are looking at choice B

B takes 36 days to finish work, then he will take 36*60/100 or 21.6 days to finish 60% of work. 
Last 12 days he has worked alone, so A has worked for 21.6-12 or 9.6 days

Now check whether A can finish the work 12 days early or in 36-12, that is 24 days. 
If the remaining 40% is done by A in 9.6 days, the entire work will be done in  9.6*\frac{100}{40}=24 days . Exactly what we were looking for.

(II) one day work

Let the time taken by B to complete the entire work be x, so A takes x-12 days. Also let both work together for y days.

We can form two equations now.

a) B finished 60% of the work in y days. 
So B will finish entire work in  y*\frac{100}{60}=x........5y=3x

b) A finished 40% in y-12 days. 
So A will finish entire work in  (y-12)*\frac{100}{40}=x-12.......5y-60=2x-24.......5y=2x+36

From a and b, we can equate value of 5y =>  3x=2x+36.......x=36

B

chetan2u · Answer

No, he does not finish the 60% in last 12 days. 
He finished 60% in x+12, where x is the number of days both A and B work together. 
You are not utilising A at all to answer your question.

I have added the method to use options to answer.

Kinshook · Answer

Working alone, B takes 12 more days than A to finish a certain job. B and A start working on the job together but A stops working 12 days before the job is done. B completes 60% of the job.

In how many days can B do the job if working alone ?

Let us assume that A can do the job in x days working alone and the work is completed after t days.

B takes y=x+12 days to finish the same job working alone.

In t-12 days, A completes = (t-12)/x = .4 
t-12 = .4x; 
x = 2.5(t-12) = 2.5t - 30

B completes remaining .6=60% in t days
1/(x+12) = .6/t 
x+12 = t/.6 = 5t/3
x = 5t/3 - 12 = 2.5t - 30
(5/2-5/3)t = 30-12 = 18
5t/6 = 18
t = 18*6/5

x = 2.5*18*6/5 - 30 = 24

B completes the job in x+12 = 36 days

IMO B

IMO D

harshitasinghal · Answer

Hi,

Let time taken by A to finish the work be x days. Then B takes x+12 days.
We are given that A stops working 12 days to the completion period when both start working on the same day.
Let t be the total time taken to complete the work.
Then
t / (x+12) + (t???12)/ x=1 (HOW DID THIS EQUATION COME UP?) WHICH FORMULA IS THIS? cAN YOU PLEASE EXPLAIN THE WORKING OF THIS SOLUTION?

Bunuel · Answer

It comes from the basic idea:
work done = rate * time

Here, x is A’s time alone, so A’s rate is 1/x.
 B’s time alone is x + 12, so B’s rate is 1/(x + 12).

B works for all t days, so B’s work is t/(x + 12).
A stops 12 days earlier, so A works for t - 12 days, so A’s work is (t - 12)/x.

Since together they finish the whole job:
t/(x + 12) + (t - 12)/x = 1

Working alone, B takes 12 more days than A to finish a certain job. B

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Working alone, B takes 12 more days than A to finish a certain job. B

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