kanika123 wrote:A merchant has 100 lbs of sugar, part of which he sells at 7% profit and the rest at 17% profit. He gains 10 % on the whole. Find how much is sold at 7% profit?
A. 70 lbs
B. 40 lbs
C. 30 lbs
D. 50 lbs
E. 60 lb
How to solve quickly?
Here's a reasonably fast approach.
First consider what would happen if half sold for a 7% profit, and the other half sold for a 17% profit.
The result would be a profit that's midway between 7% and 17%. In other words, we'd have a 12% profit.
HOWEVER, the question tells us that we get only a 10% profit.
So, we must have sold
more than half of the sugar at the lower 7% profit.
We can now ELIMINATE B, C and D.
At this point, we can test either of the two remaining answer choices (A or E). It doesn't matter which one we test. If the one we test works, we're done. If it doesn't work, we're still done, because we know the other answer is correct.
Let's test E (60 lbs sold at a 7% profit)
So, 60 out of 100 lbs sold at 7%, and 40 out of 100 lbs sold at 17%
We'll use the formula:
Weighted average = (group A proportion)(group A average) + (group B proportion)(group B average)
Weighted average = (0.6)(7) + (0.4)(17)
= 4.2 + 6.8
= 11
So, this scenario would result in a 11% profit. We want an 10% profit, so ELIMINATE E.
By the process of elimination, the correct answer is
A
If you're interested, we have a free video on weighted averages:
https://www.gmatprepnow.com/module/gmat- ... ics?id=805
Cheers,
Brent
