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Mixture and Alligation #30

30. John bought 20 kg of wheat at the rate of Rs.8.50 per kg and 35 kg at the rate of Rs.8.75 per kg. He mixed the two. Approximately at what price per kg should he sell the mixture to make 40% profit at the cost price?
A. Rs.8B. Rs.16
C. Rs.20D. Rs.12

Answer: Option D

Explanation:

CP $=20×8.5+35×8.75$
$=170+306.25=476.25$

Profit = 40%

$\text{SP }=\dfrac{(100+\text{Profit%})}{100}×\text{ CP}\\= \dfrac{(100+40)}{100}× 476.25 \\= \dfrac{140}{100}× 476.25 \\\\= \dfrac{140}{4}× 19.05 = 35 × 19.05$

Total quantity = 20 + 35 = 55 kg

SP per kg $=\dfrac{35 × 19.05}{55} = \dfrac{7 × 19.05}{11}$
$\approx \dfrac{7 × 19}{11} \approx \dfrac{133}{11} \approx 12$

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