swerve wrote:Brand A bike costs twice as much as the Brand B bike. The monthly maintenance cost of the Brand B bike is twice the monthly maintenance cost of Brand A. John purchased a Brand A bike, and Peter purchased a Brand B bike. If at any time the total expenditure on a bike is calculated as the purchase cost plus the maintenance cost up to that time, then after how many months would John and Peter have spent equal amounts on their bikes?

(1) The monthly maintenance cost of the Brand A is 5% of the cost of the bike.
(2) John and Peter purchased their bikes on the same day.

The OA is C.

Please, can anyone explain this DS question? I tried to solve it but I can't get the correct answer. I need help. Thanks.

To compare the total expenditure on the bikes, we must know the starting times, i.e., when the two bikes were purchased, the purchase price and the maintenance cost of any bike.

Let's take each statement one by one.

(1) The monthly maintenance cost of the Brand A is 5% of the cost of the bike.

Say the price of Bike B = $x; the price of Bike A = $2x; thus, the monthly maintenance cost of the Brand A bike = 5% of 2x = 0.1x, and the monthly maintenance cost of the Brand B bike = 2*0.1x = 0.2x.

Say, the total expenditure on the bikes is equal after y months after the purchase of the bikes; however, this assumption is valid if we assume that John and Peter purchased their bikes on the same day; however, we cannot assume here. Insufficient.

(2) John and Peter purchased their bikes on the same day.

Certainly insufficient. No information of the prices and maintenance costs of the bikes.

(1) and (2) together

Total expenditure on Bike A after y months = 2x + 0.1xy;
Total expenditure on Bike B after y months = x + 0.2xy;

Thus, 2x + 0.1xy = x + 0.2xy

x = 0.1xy

=> y = 1/0.1 = 10 months

Sufficient.

The correct answer: C

Hope this helps!

-Jay
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