John bought 3 brands of tea A,B and C. The cost price of the 3 brands were Sh.25,Sh.30 and Sh.45 respectively. He mixed the 3 brands in the ratio 5:2:1respectively. After selling the mixture he made a profit of 20%
a.) How much profit did he make per kg of the mixture?
b.) After 1 year the cost price of each brand was increased by12%.
(i) For how much did he sell1kg of the mixture to make 20%profit? Give your answer to the nearest 5cts.
(ii). What would have been his percentage profit if he sold 1kg of the mixture at Sh.40.25.
a) To determine the cost price per kg of the mixture, we can assume that John bought 5kg, 2kg and 1kg of brands A, B and C respectively. Therefore, the total cost price of the mixture is:
(5kg x Sh.25/kg) + (2kg x Sh.30/kg) + (1kg x Sh.45/kg) = Sh.235
The total weight of the mixture is 5kg + 2kg + 1kg = 8kg. So the cost price per kg of the mixture is:
Sh.235 ÷ 8kg = Sh.29.375/kg
The profit made per kg of the mixture is equal to 20% of the cost price per kg:
20% x Sh.29.375/kg = Sh.5.875/kg
Therefore, John made a profit of Sh.5.875 per kg of the mixture.
b) (i) After the cost price of each brand was increased by 12%, the new cost prices are:
Brand A: Sh.25 x 112% = Sh.28/kg
Brand B: Sh.30 x 112% = Sh.33.60/kg
Brand C: Sh.45 x 112% = Sh.50.40/kg
If John wants to sell 1kg of the mixture at a profit of 20%, he needs to determine the selling price:
Cost price per kg of mixture = (5kg x Sh.28/kg) + (2kg x Sh.33.60/kg) + (1kg x Sh.50.40/kg) = Sh.271.20
Profit per kg of mixture = 20% x Sh.29.375/kg = Sh.5.875/kg
Selling price per kg of mixture = Cost price per kg of mixture + Profit per kg of mixture = Sh.271.20 + Sh.5.875/kg = Sh.277.075/kg
Rounded to the nearest 5 cents, John would sell 1kg of the mixture for Sh.277.05.
(ii) If John sells 1kg of the mixture at Sh.40.25, he makes a profit of:
Profit = Selling price - Cost price = Sh.40.25 - (5kg x Sh.28/kg) - (2kg x Sh.33.60/kg) - (1kg x Sh.50.40/kg) = Sh.2.65
Percentage profit = (Profit ÷ Cost price) x 100% = (Sh.2.65 ÷ Sh.271.20) x 100% ≈ 0.98%
Therefore, if John sells 1kg of the mixture at Sh.40.25, he would only make a profit of approximately 0.98%.