A trader
has two kinds of wheat grains - one that he purchased for $20
per sack, and the other that he purchased for $12.5 per sack.
How many sacks of the cheaper wheat should he mix in 50 sacks
of the expensive wheat, so that the mixture yields a 33.33% profit
when sold at $20 per sack?
(a) 20
(b) 25
(c) 50
(d) 100
(e) 200
GMAT Test Question Solution:
Explanation: The mixture yields a 33.33% profit when sold at
$20. Hence its purchase price to the trader was $20/1.33 = $15.
This implies that the weighted average purchase price of the
two kinds of wheat grains is $ 15. We have 50 sacks of the expensive
wheat. Assume that we have n sacks of the cheaper wheat. Hence,
(12.5n + 50 x 20)/(50 + n) = 15. Simplifying this:
12.5n + 1000 = 750 + 15n
Hence, n = 100 (D)
