Question

If 8 kg of tea price costing Rs. 56 / kg is blended with 32 kg of tea of Rs. 69/ kg and 25kg of Rs. 75/kg and the mixture is sold at 20 % profit. Find the selling price (in rupees) of the mixture?

Answer 1

Hint: At first, find the total cost of each type by multiplying the rate of the type of tea with their respective rate and then add them up to find the cost price of them. Then divide it by the total amount of tea in kg to get the rate of the cost price. Then find the profit whose percent given is 20 which is calculated over cost price. After that find the selling price by having the sum of the cost price and profit.

Complete step-by-step answer:
In the question, the amount of tea and cost of each type is mentioned just like 8 kg of tea costs Rs. 56/kg is blended with 32 kg of tea of Rs. 69/kg and 25kg of tea with the rate of Rs. 75/kg. The mixture was then finally sold at a 20 % discount.
Now, at first, we will find the cost price of each type of tea which is
For the first type of tea whose quantity is 8 kg and the rate is Rs. 56 / kg, the amount will be \[8\times Rs.56\] or Rs. 448 for 8kg tea.
For the second type of tea whose quantity is 32 kg and the rate is Rs. 69/kg, the amount will be \[32\times Rs.69\] or Rs. 2208 for 32 kg tea.
For the third type of tea whose quantity is 25 kg and the rate is Rs. 75/kg, the amount will be \[25\times Rs.75\] or Rs. 1875 for 25 kg tea.
After mixing all the three types of tea, the weight of tea in kg will be 8 kg + 32 kg + 25 kg or 65 kg and their total cost price will be Rs. 448 + Rs. 2208 + Rs. 1875 or Rs. 4531.
So, we can say that the cost price of the mixture is \[\dfrac{Rs.4531}{65}\] or Rs. 6970 per kg.
The profit was 20 % and profit is calculated on the cost price. So, the profit in Rs will be
\[\dfrac{\text{Profit Percent}}{100}\times \text{Cost price}\]
\[\Rightarrow \dfrac{20}{100}\times 69.70\]
= Rs. 13. 97
Now, to find the selling price, we will take the sum of the cost price and the profit which is Rs. 69.70 + Rs. 13.94 = Rs. 83.64 / kg.
Hence, the selling price will be Rs. 83.64 / kg.

Note: One can also do it in another way, first we can find the selling price of all 65 kg tea by finding out the profit and then divide it by 65 to get the answer. But however that method would be little complex and hence students are advised to follow the above method.