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Work and ratio

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by maihuna » Thu May 07, 2009 7:58 am
A is 50% more efficient than B. C does half of the work done by A and B together. If C alone can do the work in 40 days then A B C together can do the work in how many days:

13.33
15
17.25
20
30
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by scoobydooby » Thu May 07, 2009 8:59 am
i get 13.33

C does half of the work done by A and B together
=>A+B does double C's work

if C finishes the work alone in 40 days, A+B does double the work in 40days=>A+B does the work in 20days

given, A is 50% more efficient than B=> A takes half number of days as B
let B take x days, A takes x/2 days

in 1 day, A and B does 1/x+2/x=1/20
=>3/x=1/20
=>x=60 days

in 1 day, A, B, C works=1/60+1/30+1/40=3/40 of work
=>work gets completed in 40/3=13.33 days
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by mike22629 » Thu May 07, 2009 9:25 am
Hmm..

I agree with answer but correct me if I am wrong, but you are looking for
1/A + 1/B + 1/C

So you know 1/C = 1/40
and 1/A + 1/B = 2/40 or 1/20

So 1/20+1/40 = 3/40

So total time is 40/3 or 13.333

Isn't this solution faster?

Seems like a weird question because you do not need that one piece of information.

Is this just a coincidence that my answer came up right?

Experts...
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by scoobydooby » Thu May 07, 2009 10:32 am
wow, mike22629 you sure saw through the extra info given in the problem! i like a fool read through each and every line and translated into mathematical form :(

smart thinking.
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by sureshbala » Thu May 07, 2009 12:36 pm
Folks, this can be answered much quickly.

In fact the first statement relating the efficiencies of A and B is not needed.

Given efficiency of C is half that of A and B, which mean A and B can be replaced with 2C.

Now efficiency of A,B and C is same as that of 3C i.e. thrice the efficiency of C.


Given C alone can do it in 40 days.

So time taken by 3C = 1/3 x 40 = 13.33 days
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Re: Work and ratio

by doclkk » Thu May 07, 2009 3:05 pm
maihuna wrote:A is 50% more efficient than B. C does half of the work done by A and B together. If C alone can do the work in 40 days then A B C together can do the work in how many days:

13.33
15
17.25
20
30
I'm not sure if you guys have seen the movie "little big league." But in the movie they discuss a math problem " if i can do something in 10 minutes, and you can do it 6 minutes, how long will it take for us to do together." It's the math problem before their big game.

They use a formula which has stuck with me since I was a kid. I'm surprised that in all my gmat books, I have never seen this formula used.

A*B / A+B.

This formula only works with two variables.Either that, or I just don't know how to apply it with 3.

AB does it in half the time C does it - so essentially you have TWO variables.

So let AB = A and let C = B.

A*B / A+B = 20*40 / 20+40 = 800 /60 or 80/6 or 40 / 3 or 13 1/3.

This I find is the EASIEST formula to remember. Take a break, watch the movie and then you will have one less formula to remember because the formula will leave an indellible mark in your brain.
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Re: Work and ratio

by Ian Stewart » Thu May 07, 2009 5:13 pm
doclkk wrote:
They use a formula which has stuck with me since I was a kid. I'm surprised that in all my gmat books, I have never seen this formula used.

A*B / A+B.
I'd guess you have seen this formula in your GMAT books, just written in a different way. Your version of the formula:

T = AB/(A + B)

is actually identical to this version, which I've seen more often in print:

1/T = (1/A) + (1/B)

Notice with this second formula above, if we get a common denominator on the right, we have:

1/T = (B/AB) + (A/AB)
1/T = (A + B)/AB

and finally, taking reciprocals on both sides, you have:

T = AB/(A + B)

which is the version of the formula you've used.

_____

For two worker problems, I think your version of the formula is easier to work with - using it, you solve for T directly, without needing to take a reciprocal at the end. That said, it's much harder to remember the three-worker version of the formula in the T = ... form, while it's relatively easy to remember 1/T = 1/A + 1/B + 1/C (you can work out the T = ... version of this by following the same steps I did above). That's likely the reason most prep books teach the 1/T = ... version of the formula.

And all of that said, you don't need a formula at all to solve combined rates problems, as I've explained in other posts.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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