July 11th Quiz: Question 2 - Savings from the wage increase

[emperor]

Two workers A and B have their monthly wages increase by 20% and 30% respectively in July as compared to their monthly wages in June. If their monthly expenses increase in the ratio of 10% and 20% respectively in the month of July as compared to that in June, by what percentage has their respective savings increased in July as compared to that in June?

(A) 10% and 10% respectively
(B) 2% and 6% respectively
(C) 8% and 4% respectively
(D) 12% and 26% respectively
(E) Insufficient data

The correct answer is E. Could anyone explain how?

Is it because that the question stem does not provide what the denominator should be for percentage of savings? In other words, the question asks to find the percentage of savings, but the percentage of savings with referring to what?

I originally thought that the stem refers to savings from monthly wages after expenses. Based on that, I got 8 1/3% for A and 8 9/13% for B. Clearly, there is no choice representing my answer. Any thoughts?

[ksb]

Hi

The answer to the above question is Insufficient Data as the question does not state what percentage of the wages was saved by the workers in June.

Let us take some numbers.

Let us say, A's wages is $100 and let A's expenses be $80 in June. Therefore, savings in June is $20.

Further, A's wages in July will be $120 (20% increase) and A's expenses in July will be $88 (10% increase). Hence, savings is 120 - 88 = $32 i.e., an increase of 60% in savings.

On the contrary, let us assume A's expenses in June to be $50. Therefore, savings in June is $50.

A's expenses in July will be $55 and savings will therefore, be $120 - $55 = $65 i.e., an increase of only 30%.

Depending upon how much (% of wages) each of them saved in June, the value of the % increase in savings changes.

Hope this clears the doubt.

KSB

[emperor]

Thanks Baskar.

Initially, I misconstrued the question. Upon re-reading, I understand that the question is about percentage increase in savings from June to July.

As you pointed out, we need the percentage of June's savings after its expenses in order to determine the increase in savings percentage from June to July.