If 20% of certain quantity of work is done by A and the rest by B,

Question

If 20% of certain quantity of work is done by A and the rest 80% by B, the work is completed in 20 days. If 80% of the work is done by A and the remaining 20% by B, then the work is completed in 30 days. How many days are required to complete the work , if A and B work together.

Hi Karishma,
I think in the last step, it should be 3/50 + 3/100 instead of 3/40+3/100. Please check.
A. 11 1/9
B. 10 1/9
C. 12
D. 15

Source: TIME material.

A. 11 1/9
B. 10 1/9
C. 12
D. 15

Source: TIME material.

KarishmaB · Accepted Answer

Using the formula: Work = Rate * Time
Time = Work/Rate

Assume A's rate of work is A. 
Assume B's rate of work is B.

A does 20% of the work. So if work is 1, A did .2 of the work.

Days for which A worked + Days for which B worked = Total Days (since they work successively)

Work of A/Rate of A + Work of B/Rate of B = Total Days

.2/A + .8/B = 20

KarishmaB · Answer

Use algebra:

0.2/A + 0.8/B = 20
1/A + 4/B = 100

0.8/A + 0.2/B = 30
4/A+ 1/B = 150

15/B = 250
B = 3/50 work per day
A = 3/100 work per day

Combined rate = 3/40 + 3/100 = 9/100
Time taken when working together = 100/9 = 11(1/9) days

Answer (A)

It is not a GMAT type question. For GMAT, it's best to stick to GMAT material.

Alex75PAris · Answer

Hello Karishma

Can you please explain how you get this : "0.2/A + 0.8/B = 20" ?

Thanks,

Alex

Alex75PAris · Answer

Thank you ! it's clear now

pourts · Answer

Would anyone be willing to explain why my method didn't work, and why I got a wrong answer?

Eq #1: 0.8 = B *20
Eq #3: 0.8 = A* 30

Solve Eq #1: B = 1/25 = 3/75 using 75 as a common denominator
Solve Eq #2: A = 2/75

Combined rate is 5/75. At a rate of 5/75 they will finish in 75/5 = 15 days.

How come this isn't correct?

ravindra88 · Answer

Because A & B are not working simultaneously in given situations. So assuming that B took 20 days to finish 80% of the work is wrong because B would have worked lesser number of days than that and same is true with A. You can assume it like B started the work, left it at some point and immediately A took over.

exc4libur · Answer

rate•time=work

1/5/a+4/5/b=20…1/5a+4/5b=20…b+4a/25ab=20
4/5/a+1/5/b=30…4/5a+1/5b=30…4b+a/25ab=30
4b+a/30=b+4a/20…80b+20a=30b+120a…b=2a
1/5a+4/5b=20…1/5a+4/5(2a)=20…a=3/100
t=1/a+b…t=1/a+2a…t=1/3a…t=1/3(3/100)
t=11+1/9

Ans (A)

aaditya005 · Answer

Hi Karishma,
 I think it should be 3/50+3/100 instead of 3/40+3/100. Please check.

gvij2017 · Answer

Could you tell me where I am wrong.

I wrote equations like this.

1/5a + 4/5b = 1/20 
4/5a + 1/5b = 1/30

I add up both equations and got 
1/a + 1/b = 50/600

Here I got A and B did the job in 12 days.

How I did it wrong!

hkkat · Answer

Use algebra:

0.2/A + 0.8/B = 20
1/A + 4/B = 100

0.8/A + 0.2/B = 30
4/A+ 1/B = 150

15/B = 250

sorry guy and  VeritasKarishma , how did it end up becoming 15/B = 250?
Thank you for your time!!

KarishmaB · Answer

We solved the two simultaneous equations:

1/A + 4/B = 100 ... (I)
4/A+ 1/B = 150 ...(II)

(i) * 4 - (II)

4/A + 16/B = 400
-4/A - 1/B = -150

You get 15/B = 250

plaverbach · Answer

I did the sum and ended up with:
 \frac{1}{A}+\frac{1}{B}=50

Times 2:

\frac{2}{A}+\frac{2}{B}=100

You can subtract this equation in any of the below:
 \frac{2}{A} + \frac{8}{B} = 200

\frac{8}{A} + \frac{2}{B }= 300

That helped me find A and B, but it might not be the fastest route...

plaverbach · Answer

I made the same mistake,  VeritasKarishma  , can you help us?

KarishmaB · Answer

plaverbach

What are your variables a and b here? Are they the time taken by A and B each independently or are they the rates of A and B?

From your equation I would guess that a and b are the time taken by A and B independently because you equated their sum to 1/20, which is the average rate. But note that this is not combined rate because they are not working together at their individual speeds. First A does 20% of the work at her speed and then B does 80% of the work at her speed. This is obvious from the way the question is worded - A does 20% and B does 80%. Then A does 80% and B does 20%
But if they were working simultaneously at their constant rates, each would do the same fraction of work in every case. How can A do 20% of work in one case and 80% in another case? This means A does 20% work first in some days and then B does the rest 80% in some more days and total adds up to 20 days.

As I said, this is not GMAT material. You set yourself up for confusion when you invest your time in working on non-GMAT material.

plaverbach · Answer

THANKS, just thanks!
I've learned a lot here...

AdityaVerma21 · Answer

The Combined rate is 3/50+3/100 instead of 3/40+3/100.

Kunal1801 · Answer

Can't understand why the answer is A and not C
Through my working:
Let A's work be x and B's work be y
1/5x+4/5y=1/20 (St.1)
4/5x+1/5y=1/30 (St 2)
St 1
through lcm we get
(x+4y)/5=1/20 which turns to 20x+80y=5 which can be written as 4x+16y=1 (St 3)
same goes with second Statement and we get 120x+30y=5 which can be further written as 24x+6y=1 (St 4)
St 3 multiplied by 6 subtracted by St 4
we get 90y=5. y=1/18
substitute the value of y in any of the equations we get the value of x as 1/36
Therefore 1/36+1/18= 3/54 =1/18

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