Working alone at their respective constant rates, A can complete a tas

Question

Working alone at their respective constant rates, 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

Are You Up For the Challenge: 700 Level Questions

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

Are You Up For the Challenge: 700 Level Questions

Archit3110 · Accepted Answer

rate of A = 1/a
and rate of B = 1/b
if a starts work it completes in 1,2 , 5,6 , 9,10 = 6 days
and b in 3,4 , 7,8 ; 4 days 
6/a + 4/b = 1---(1)
and if b starts work we will have b rate ; 6/b and a ends with half day more ; 4.5/a
6/b+4.5/a=1--(2)
solve for 1 &2
we get 
a=9 and b = 12
so combined rate = 1/9+1/12 = 7/36
36 /7 days IMO D

lacktutor · Answer

If A starts:
—> 2(1/a)+ 2(1/b)+ 2(1/a)+ 2(1/b)+2(1/a)= 1

If b starts: 
—> 2(1/b)+ 2(1/a)+ 2(1/b)+2(1/a)+2(1/b)+(1/2)(1/a)= 1

6(1/a)+ 4(1/b)= 1
6(1/b)+ (9/2)(1/a)=1

—> a= 9
—> b= 12

(1/a) + (1/b)= 1/x
1/9+ 1/12= 21/108= 1/x
—> x= 108/21= 36/7

The answer is D

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wishmasterdj · Answer

I am going to ask a very silly question here. How did you solve the 2 equations. I couldn't get the values of a and b, even after doing everything right upto that point.

MBAB123 · Answer

wishmasterdj 
eq1 = 6b +4a = ab and eq2 = 6a+ 4b = ab. 
Subtract Eq1 from eq2

2a-1.5b = 0. Hence, 2a=1.5b......... Eq3.

Use Eq3 in either Eq1 or Eq2 and you'll get your answer.

Let me know if any step isn't clear!

Bambi2021 · Answer

One thing that I dont understand here. Why do you choose 6/a and 4/b and not 6*a and 4*b?

I want to take 6 times "the working rate of b" + 4 times "the working rate of a" = 1 unit

(units/day)*days = units

Seems most logical to me...

6a + 4b = 1
4,5a + 6b = 1 
-->
1,5a = 2b and a = 4b/3
-->
24b/3 + 12b/3 = 1 
-->
36b/3 = 1 --> 36b = 3 --> b = 12 days

Thekingmaker · Answer

i didn't go with calculating the entire days they were working which was too much work i said another method however to be on the saver side it's do what has been optimised 43/40 only thing which was close was 36/7

Raunak2794 · Answer

can you please tell why did you equate the equation (1) to 1 and not 1/10? Similarly equation (2) to 1?

rsrighosh · Answer

How much time did it take to get the answer?..... setting up equation and calculation took me a lot of time... 4 mins..

any tips on this?

NILZOZO · Answer

If A works first, A does that in 6 days and B in 4 days
If B works first, B does that in 6 days and A in 4.5 days

ATQ, 6A+4B=4.5A+6B
 => 1.5A=2B
Thus, A:B=4:3

So, Total works = 6*4 + 4*3 =36

Time = 36/(4+3)=36/7. (ans)

GmatPoint · Answer

Let the total units of work be a*b.
Thus, A does ‘b’ units of work per day, and B does ‘a’ units of work per day.

Now in the pattern of work mentioned in the first case, A will work for 6 days and B will work for 4 days.

Total work done = 6b + 4a

Thus, 6b + 4a = ab....(i)

For the second case, B will work for 6 days, and A will work for 4.5 days.

Thus, 4.5b + 6a = ab.....(ii)

From (i) and (ii),

6b + 4a = 4.5b + 6a
1.5b = 2a....(iii)

Putting the value in equation (i),

8a + 4a = (2/1.5)*a^2
12 = (2/1.5)*a
a = 9

Thus, b = 12

Total work = 108

If A and B work together, the Total days to finish the work = 108/21 = 36/7

Thus, the correct option is D.

samarpan.g28 · Answer

Efficiency = 1/time to complete a work.
Efficiency of A = 1/a, efficiency of B = 1/b.
Let's go by this at first "If A starts they finish the task in exactly 10 days" so the pattern becomes AA BB AA BB AA i.e. A works for 6 days and B works for 4 days.
Our first equation is  6/a + 4/b =1 where 1 is total amount of work.
The second statement given is "If B starts, they take half a day more" so the pattern is BB AA BB AA BB A(for 0.5 days).
Our second equation is  6/b + 4.5/a =1.
Solve the equations and we will get a=9 and b=12.
Thus, if A and B work together then their total efficiency is  1/9 + 1/12 = 7/36 .
Therefore, they take together  36/7  days. Option (D) is correct.

AKukreja · Answer

Bunuel  I reached the point of calculating a:b. However, I was getting a:b as 15:20 i.e. 3:4 which is somehow equivalent to 9:12 which is the answer that people are getting. But when I finally calculate the number of days, I do 1/3+1/4= 7/12. Hence, my answer of number of days would be 12/7. Where am I going wrong? Thanks in advance!

Working alone at their respective constant rates, A can complete a tas

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