# Word Problem 13 ( Gain or loss percentage calculation)

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%

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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