Question

Ravi bought $ 30kg $ tea at ₹ $ 80 $ per $ kg $ and $ 50kg $ tea at ₹ $ 50 $ per $ kg. $ He mixed both the varieties of tea and sold it at ₹ $ 75 $ per $ kg. $ Find his gain or loss percent?

Answer 1

Hint: Calculate the total cost price of each variety. Use that information to calculate the total cost price of the mixture. Then use the formula for profit or loss percent.

Complete step-by-step answer:
Let Ravi bought two varieties of tea,
 $ {T_1}: $ $ 30kg $ tea at ₹ $ 80 $ per kg
And
 $ {T_2}: $ $ 50kg $ tea at ₹ $ 50 $ per kg.
After that, he mixed both the varieties of tea and sold it at ₹ $ 75 $ per kg.
For $ {T_1}: $ Cost price of \[1{\text{ }}kg{\text{ }} = \] ₹ $ 80 $
Then cost price of $ 30kg = 30 \times 80 $
 $ = $ ₹ \[2400\]
For $ {T_2}: $ Cost price of \[1kg\] $ = $ ₹ $ 50 $
Then cost price of \[50kg = 50 \times 50\]
 $ = $ ₹ $ 2500 $
Therefore, the total quantity of tea \[ = 30kg + 50kg\]
\[ = 80kg\]
Therefore,
The total cost price of $ 80kg $
= Cost price of $ 30kg + $ Cost price of $ 50kg $ .
 $ = 2400 + 2500 $
 $ = $ ₹ $ 4900 $
Profit can be calculated by the formula
 $ \Rightarrow profit\% = \dfrac{{S.P. - C.P.}}{{C.P.}} \times 100 $ . . . (1)
Where,
S.P. is the selling price
C.P. is the cost price
Ravi sold the mixture at ₹ 80 per kg
Therefore, Selling price of mixture of $ 80kg = 75 \times 80 $
 $ = $ ₹ $ 6000 $
Therefore, from equation (1), we get
 $ \Rightarrow profit\% = \dfrac{{6000 - 4900}}{{4900}} \times 100 $
 $ = \dfrac{{1100}}{{4900}} \times 100 $
 $ = \dfrac{{11}}{{49}} \times 100 $
 $ = \dfrac{{1100}}{{49}} $
 $ = 22.44 $
Therefore, Ravi will make a profit of $ 22.44\% $

Note: Gain and profit are the same thing. Do not get confused with it. If (S.P. – C.P.) would have been negative, then Ravi would have made negative profit. Means that answer would have been his loss percent. In this type of question, it is important to understand that you have to calculate the total cost price rather than the cost price per kg. Finding the total cost price will help to get the total cost price of the mixture, which will then be used to solve the question.