Jack can do a certain job in 20 days while Tom can do the same job in 25 days. If both do the job together and are paid a total amount of Rs 450. Find the amount that should be given to Jack (assuming that each person is paid according to the ratio of the job done).

A) 200
B) 250
C) 360
D) 380
E) 400

My answer is 200. Please correct me if i m wrong. Thanks

ANS: 250.
Money will be distributed in ratio of work done by both.
Wj / Wt = (1/20)/(1/25) = 5/4
Hence Jack will get (5/9)* 450 = 250

200 cant be the answer as jack works only in 20 days and tom in 25 days hence jack should be paid more.

Jack can 1/20 work in 1 day and tom can do 1/25 work in 1 day.

Combined both can complete the work in 100/9 days.

Jack share in 1 day=1/20*450

for 100/9 days= 1/20*450*100/9

=250

Here is my solution

Work done by Jack in one day = 1/20 (as he takes 20 days to finish the job)
Work done by Tom in one day = 1/25

Total work that can be done by both when they work together =
1/20 + 1/25 = 45/(20*25) = 9/100

The amount of work completed by Jack in one day (when both work together is) = (1/20)/(9/100) = 5/9
The amount of work completed by Tom in one day (when both work together is) = (1/25)/(9/100) = 4/9

ratio for jack's portion of work is 5/9

so his share is = 5/9 *450 = 5*50 = 250 (Answer)

jack 20 days
tom 25 days

let work done be x
jack does 5x work and tom does 4x work

9x=450
x=50
jack =250

We don't want to do a bunch of math unless we have to. If we can reason it out with a minimum of math, all the quicker, and therefore all the better. Thus, I'll endorse gmatjedi and akdayal's approach.

Let's reason it out.

Pretend for a moment that Jack can do the job in 1 day while Tom in 2. Then, isn't it clear that Jack works 2/1 times as fast as Tom?

Because Jack in fact does the job in 20 days while it takes Tom 25, Jack works 25/20 or 5/4 times as fast as Tom

Thus, towards the whole job, Jack contributes 5 units for every 4 units contributed by Tom.

In other words, they contribute in a 5:4 ratio, which is a part to part ratio, Jack's part: Tom's part. Thus, the part to final ratio (Jack: Jack + Tom) is just 5/9. And, so, Jack deserves 5/9 of the 450 rupees.

Testluv, I understood ur approach but im doing the mistake in ratios here...I am assuming that because J can do the job in 20 days while T in 25, then J:T is 20:25 which is equal to 4:5, so Jack is contributing 4 out of the 9 not the other way around...I know it doesnt make sense logically cuz he's faster, but from a math point of view, where am I doing the mistake exactly?

Thouraya wrote:Testluv, I understood ur approach but im doing the mistake in ratios here...I am assuming that because J can do the job in 20 days while T in 25, then J:T is 20:25 which is equal to 4:5, so Jack is contributing 4 out of the 9 not the other way around...I know it doesnt make sense logically cuz he's faster, but from a math point of view, where am I doing the mistake exactly?

J:T=25:20 or 5:4
ratio of money will be amount of job done

Thouraya wrote:Testluv, I understood ur approach but im doing the mistake in ratios here...I am assuming that because J can do the job in 20 days while T in 25, then J:T is 20:25 which is equal to 4:5, so Jack is contributing 4 out of the 9 not the other way around...I know it doesnt make sense logically cuz he's faster, but from a math point of view, where am I doing the mistake exactly?

Well, let's say Jack's time is 1 day, and Tom's is 2 days. Then it is clear that Jack works twice as fast as Tom, and so J:T contribute in 2:1 ratio.

Let's say that Jack's time is 1 day, and Tom's is 3 days. Then it is clear that Jack works thrice as fast as Tom, and so J:T contribute in 3:1 ratio.

Let's say that Jack's time is 20 days, and Tom's is 25 days. Then, Jack works 25/20 times as fast as Tom, and so J:T contribute in 25:20 ratio or 5:4 ratio.

Work contributed is proportional to rate of work. But rate of work is inversely proportional to time of work (if you do the job in half as much time as me, then you work twice as fast me).

Hi,

I don't understand this problem; is it considered a difficult one or might come across it in a 650 level?

Why can't we deal with it as a regular rate/work problem? Then in 1 hour, Jack can do 1/20 and Tom 1/25..I don't know how to proceed though. I would grealy appreciate any help