Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. Th

Question

Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?

A. 46/9
B. 50/9
C. 50/11
D. 36/7
E. 210/41

A. 46/9
B. 50/9
C. 50/11
D. 36/7
E. 210/41

tslaxz · Accepted Answer

A can complete 1/a of the task daily
B can complete 1/b of the task daily

By the two statements (starting with A they complete the task in 10 days and starting with B they complete in 10,5 days), we have:
I. 6/a + 4/b = 1
II. 6/b + 4,5/a = 1

=> 6/a + 4/b = 6/b + 4,5/a => (6b + 4a)/ab = (6a + 4,5b)/ab => 2a = 1,5b => b = 4a/3 (III)

Substituting it in the equation 1: 6/a + 4/(4a/3) = 1 => 6/a + 3/a = 1 => 9/a = 1 => a = 9
Substituting it in the equation III again: b = 4*9/3 => b = 12

Considering the values of A and B, they would be able to complete 1/9 + 1/12 = 7/36 of the task daily, so they would take 36/7 days to complete the task.

Answer: D

chetan2u · Answer

Hi,

firstly it is a tough Q.. 
  if one is clueless where to start, we can work on the info and easily eliminate three choices B,C, and D, and E too can be eliminated after a bit of thought...

IN first case A working for 6 days and B for 4 days, work is completed and in second case A for 4.5 days and B for 6 days, wk gets completed..
so if we combine A for 10.5 days and B for 10 , wk can be completed twice ...
so wk to be completed once, A requires to work for 5.25 days and B for 5 days...

what can we make out ..

1) if both A and B work for 5 days, the work will not be completed, as we have to add .25 day work of B to it.. C (50/11)<5 is out...

2) work will be completed before (5+5.25)/2 days, as work of .25 days of A is being done by both together and A is faster than B..
so total time will be greater than 5.125 and should be less than 5.25, when A is faster than B .. 
so following can be eliminated
A 46/9=5.111 <5.125 
B 50/9=5.55>5.25

E 210/41= 5.122<5.125..

D 36/7=5.14...CORRECT .. between 5.125 and 5.25 is the answer..

answer can also be arrived at by proper work-time method.  
IN first case A working for 6 days and B for 4 days, work is completed 
or 6/a +4/b=1..(i)

and in second case A for 4.5 days and B for 6 days, wk gets completed..
so 4.5/a+ 6/b=1..(ii)

or 6/a +4/b= 4.5/a+ 6/b...
we get a=3b/4 here ..
substitute this value in (i)..
24/3b +4/b=1...
this will give us b as 12..
so a= 3b/4=9..

we have to find 1/a+1/b as one day work of both.. 
1/12 + 1/9= (3+4)/36= 7/36..
so time taken = 36/7
D

chetan2u · Answer

hi  Bunuel ,
THanks for such a lovely Q.. Edited

Bunuel · Answer

The answer is given as D. I think you should check the highlighted part.

tryambaks · Answer

Answer is (D)
A does 1/a part in 1 day =2/a part in 2 days
Similarly B does 2/b part is 2 days
When A starts 
2/a+2/b+2/a+2/b+2/a=1 => 6/a+4/b=1 .....................(1)

When B starts 
2/b+2/a+2/b+2/a+2/b+ 1/2a  (Half days work)  =1 => 2/b=3/2a ..................(2)

Solving (1) and (2)
we get a=9 and b = 12

A and B together does the work in ab/a+b =108/21 =36/7 days

Hence Answer is (D)

gracie · Answer

equation1: 6/a+4/b=1
equation2: 9/a+12/b=2
solving, a=9;b=12
let d=days for A and B to complete task working together
d(1/9+1/12)=1
d(7/36)=1
d=36/7 days

Tmoni26 · Answer

So I started and got the following equation, would love to get help on where I have gone wrong
6/a + 4/b = 1/10
That is 6 * 1/a (rate of A) and 4 * 1/b (rate of B) = 1/ 10 (overall time utilised)

second equation followed the same route, is my equation wrong??

KarishmaB · Answer

When A starts, A works for 6 days and B for 4 days to complete the work. 
6/a + 4/b = 1 Work

When B starts, A works for 4.5 days and B for 6 days to complete the work. 
4.5/a + 6/b = 1 Work

Solving these two equations simultaneously, we get:
18/a + 12/b = 3
9/a + 12/b = 2
9/a = 1
a = 9
b = 12

Rate of work while working together = 1/9 + 1/12 = 7/36
Time taken to complete the work = 36/7 days
Answer (D)

Mathivanan Palraj · Answer

Let their efficiency ratio be a:b
Therefore, 6*a+4*b=4.5*a+6*b
=>a to b is 4:3
Number of days taken will be 3*k and 4*k, where k is a constant.
If they work together they take (3*k)*(4*k)/3*k+4*k = 12*k^2/7*k = 12*k/7
Look at the option. Only D could be the correct one.

23ss23 · Answer

Q. Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?

Sol: The rate of work and all the fractions might look a little confusing, so I tried to break it down in simple terms.

Scenario 1 - A starts and proceeds to work for two days, followed by B who also works for 2 days. In this case, the work is completed in 10 days. Which means A has worked for 6 days and B has worked for 4 days (A,A,B,B,A,A,B,B,A,A).

Scenario 2 - B starts and proceeds to work for two days, followed by A who also works for 2 days. In this case, the work is completed in 10.5 days. Which means A has worked for 4.5 days and B has worked for 6 days.

Now, if we equate both scenarios, we get - 6A + 4B = 4.5A + 6B. Solve the equation and you get - A:B = 2:1.5 (or 4:3).

Since we have the ratio of their efficiencies, we can use the same get an estimate of the work done. For eq, since the ratio of their efficiencies is 4:3, we can go ahead with the assumption that A has done 4 unites of work per day, while B has done 3 units of work per day. Substitute these values in one of the scenarios, and you get the total work done.

6A + 4B (scenario one) can be written as 6*4 + 4*3 = 36. Now, that we have the total work, simply divide this by the work that can by A & B in a day if they work together, which is 4+3 = 7.

Now, to find the number of days required to complete the task if they both work together, we just have to divide the total work by the work that can by A & B in a day if they work together => 36/7

I tried to make it as elaborate as possible to make it easier to understand each step, so that it'll be easier for you to remember and replicate. Once you get a hang of it, this should not take more than a minute to solve.

Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. Th

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