Civil Engineering > GATE 2025 SET-2 > Ratio and Proportion
A business person buys potatoes of two different varieties P and Q, mixes them in a certain ratio and sells them at 192 per kg.
The cost of the variety P is 800 for 5 kg.
The cost of the variety Q is 800 for 4 kg.
If the person gets 8% profit, what is the P:Q ratio (by weight)?
The cost of the variety P is 800 for 5 kg.
The cost of the variety Q is 800 for 4 kg.
If the person gets 8% profit, what is the P:Q ratio (by weight)?
Correct : a
The cost per kg of each variety
Variety P: 800 for 5 kg
Cost per kg of P = 800 ÷ 5 = 160/kg
Variety Q: 800 for 4 kg
Cost per kg of Q = 800 ÷ 4 = 200/kg
The cost price of the mixture
Given: Selling price = 192 per kg and Profit = 8%
Using the formula: SP = CP × (1 + profit%)
192 = CP × 1.08
CP = 192 ÷ 1.08 = 1600/9 per kg
Using the mixture rule
Let the ratio of P:Q be x:y (by weight)
Cost of mixture per kg = (x × 160 + y × 200) ÷ (x + y)
This should equal 1600/9:
(160x + 200y) ÷ (x + y) = 1600/9
9(160x + 200y) = 1600(x + y)
1440x + 1800y = 1600x + 1600y
1800y - 1600y = 1600x - 1440x
200y = 160x
y/x = 160/200 = 4/5
Therefore, x:y = 5:4
Answer: P:Q = 5:4
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