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%

Question

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.

Answer 1

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%.