How Many Kilograms of Sugar Costing ₹9 per Kg Must Be Mixed with 27 Kg of Sugar Costing ₹7 per Kg So that There May Be a Gain of 10% by Selling the Mixture at ₹9.24 per Kg? - Mathematics

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MCQ

How many kilograms of sugar costing ₹9 per kg must be mixed with 27 kg of sugar costing ₹7 per kg so that there may be a gain of 10% by selling the mixture at 9.24 per kg?

Options

  • 36 kg

  • 42 kg

  • 54 kg

  • 63 kg

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Solution

63 kg
Explanation:
SP of 1 kg of mixture = ₹9.24
Gain= 10%
∴ CP of 1 kg of mixture

= `(100/110xx9.24)=`₹8.40

By the rule of alligation, we have

\[\begin{array}{cc}
₹9\phantom{...........}₹7\\
\setminus \phantom{............}/ \\
\ce{\underset{₹8.40}{Mean Profit}}\\
/\phantom{............} \setminus \\
₹1.40 \phantom{..............}₹0.60
\end{array}\]
∴ Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3

Let x kg of sugar of 1st be mixed with 27 kg of 2nd kind.

Then, `7:3=x:27`

⇒ `x=((7xx27)/3)`

= 63kg

Concept: Ratio and Proportion (Entrance Exam)
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