Percentage - Profit and loss question

Question

I bought 3 mangoes and 5 oranges at Rs. 67. After eating 1 mango, I sold the remaining fruits to Raj at Rs. 67, Raj after eating 1 mango and 1 orange, sold the remaining fruits to Ram at Rs. 67, if Raj had an effective profit of 35% in this manner, how much percentage profit did i earn?

Answer 1

Let m equal the value of a mango in Rs. and let r equal the value of an orange (‘o’ can cause confusion with zero). Therefore, 3m + 5r = 67 as you bought 3 mangoes and 5 oranges for Rs. 67. As Raj made a 35% profit, 2m + 5r = 1.35(m + 4r). Thus, we have the following equations:

3m + 5r = 67

1.35(m + 4r) = 2m + 5r

Solving for m in terms of r:

3m = 67 - 5r

m = (67 - 5r)/3

Substituting m for r:

0.35(m + 4r) = m + r

0.35((67-5r)/3 + 4r) = (67-5r)/3 + r

Solving for r, we get:

r = 871/89

Substituting for m:

m = 536/89 Your percentage profit was:

100(67/(67-m))-100=(100*(67-(536/89)))-100 = (800/81)% = 9.88% (3sf)

Therefore, you made approximately 9.88% profit.