Word Problem 13
Problem 13: A man buys a certain number of oranges at 24 a rupee and an equal number at 30 a rupee. He mixes these at 27 a rupee. What does he gain or loss percent?
a. 1-19/81% b. 1-5/7% c. 5-1/2% d. 5-1/3%
GRE arithmetic questions and answers
Solution:
Suppose the man buys ‘y’ number each rated type of oranges
then for 24 a rupee oranges we can write;
Similarly for 30 a rupee oranges we write;
So, cost prices for y oranges of 24 a rupee type and y oranges of 30 a rupee type are y/24 and y/30 rupees respectively.
Now total cost price for both type of oranges is;
Now the man mixes both types oranges which become 2y in number. He sells these at 27 a rupee rate.
for sale price of 2y oranges at this rate we can write;
so mixed oranges sale price is
Here we can see now that CP is greater than SP i-e total cost price for individual type is greater than sale price for mixed oranges. It means he is earning no profit but a loss !
formula for loss is
or
Now formula for loss %age is
Putting values of loss L and cost CP from above
After simplification we get;
So, the option ‘a’ is correct answer
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