NECO 2002 Mathematics · Question 10

Three sets of rice x, y and z are sold for N15.00, N35.00 and N60.00 respectively per kg. It they are mixed in…

Question

Three sets of rice x, y and z are sold for N15.00, N35.00 and N60.00 respectively per kg. It they are mixed in the ratio of 1: 3 : 2, what is the cast per kg of the mixture?

A.N45.00
B.N42.50
C.N40.00
D.N35.50
E.N25.80

Answer: C. N40.00

Explanation written with AI and checked against the answer key

Analyze the question: Three types of rice with different prices per kg are mixed in the ratio 1 : 3 : 2. We need the cost per kg of the mixture.

Concept: The cost per kg of a mixture is the total cost of all parts divided by the total number of parts (a weighted average):

Cost per kg = (total cost) ÷ (total quantity)

Solution:

Take 1 kg of x, 3 kg of y and 2 kg of z.

x: 1 × 15 = N15
y: 3 × 35 = N105
z: 2 × 60 = N120

Total cost = 15 + 105 + 120 = N240

Total quantity = 1 + 3 + 2 = 6 kg

Cost per kg = 240 ÷ 6 = N40.00

Tip: For mixture problems, multiply each price by its ratio part, add them up, then divide by the sum of the ratio parts. Always check that your answer lies between the cheapest (N15) and the dearest (N60) price. N40 does, so it is sensible.

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