Problem Solving

Getting the same time, 6 minutes, for both:

Tom chops 4 lbs in 6 minutes
Tammy chops 9 lbs in 6 minutes

So when they work for the same amount of time, the ratio of the amount Tammy chops to the amount Tom chops is 9 to 4, and since 9 is 125% greater than 4, the answer is 125%. The 65 lbs in the question is irrelevant.

swerve wrote:When Tom works alone he chops 2 lbs salad in 3 minutes, and when Tammy works alone she chops 3 lbs salad in 2 minutes. They start working together, and after some time finish chopping 65 lbs of salad. Of that 65 lbs, the salad quantity chopped by Tammy is what percent greater than the quantity chopped by Tom?

A. 44%
B. 100%
C. 125%
D. 225%
E. 400%

The OA is C

Source: Economist GMAT

We use the "percent greater than" formula: (Tammy's rate - Tom's rate)/Tom's rate x 100%.

Since Tom's rate is 2/3 and Tammy's rate is 3/2, when they work together, Tammy's work will always be:

(3/2 - 2/3)/(2/3) x 100

(9/6 - 4/6)/(2/3) x 100

(5/6)/(2/3) x 100 = 5/6 x 3/2 x 100 = 15/12 x 100 = 5/4 x 100 = 125% greater than Tom's.

Alternate Solution:

In 6 minutes, Tom will chop 4 lbs of salad, and Tammy will chop 9 lbs of salad. Together, they chop 4 + 9 = 13 lbs of salad. Notice that, of the 13 lbs salad chopped, 4/13 is chopped by Tom and 9/13 is chopped by Tammy. As long as they work for an equal amount of time, the ratio of salad chopped by each will be the same; therefore, of the 65 lbs. of salad that they chopped together, 65 x 4/13 = 20 lbs are chopped by Tom and 65 x 9/13 = 45 lbs are chopped by Tammy.

Therefore, Tammy chopped 100*[(45 - 20)/20] = 100 * (25/20) = 125% more than Tom.

Answer: C