Problem Solving

Hello,

Can anyone explain the resolution to the below problem:

Alice's take home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did not save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?
a. ½
b. 1/3
c. ¼
d. 1/5
e. 1/6

Thanks.

Hi pratyoosh,

This question was discussed many times in BTG.Please search it.you ll find tons of solutions.

If u still have doubts please let us know.

pratyoosh wrote:Hello,

Can anyone explain the resolution to the below problem:

Alice's take home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did not save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?
a. ½
b. 1/3
c. ¼
d. 1/5
e. 1/6

Thanks.

We can plug in the answers, which represent the fraction saved each month.

Plug in monthly pay = 60.

Answer choice C:
1/4 * 60 = 15 saved each month, 45 not saved.
12*15 = 180 total saved for the whole year.
(Total saved)/(monthly not saved) = 180/45 = 4. We need her to save less.

Answer choice D:
1/5 * 60 = 12 saved each month, 48 not saved.
12*12 = 144 total saved for the whole year.
(Total saved)/(monthly not saved) = 144/48 = 3. Success!

The correct answer is D.

If the options had 4/5 as one of them, i would have blindly marked 4/5 as my answer..
However, 1/5 is the answer

Good Qn..

let P - Payment per month.

Savings = P-nP ; n- fraction

from the Qn ,

The total amount of money that she saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did not save.

12 * per month Savings = 3 ( amount that she did not save every month)

12* (P-nP) = 3 * P-[P-(P-nP)]

On solving we get n=4/5...( as soon as i got this, i searched for 4/5 in the options.., couldnt find it.. re-read the Qn and then solved it further)

Qn is "what fraction of her take-home pay did she save each month"

i.e Savings??? ---> P-nP= P-(4/5)P=P/5 --> Answer D

Thank you Mitch and Ymach3, most useful.

Regards,
Pratyoosh.