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

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.

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!

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

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

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

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?

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)

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.

 

­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.