Question:medium

A grocer mixes coffee powder of 2 types, one of which is priced at Rs.\ 60 and the other at Rs.\ 90. What should be the ratio of combining the two, to sell the blended mix coffee powder of the two types at Rs.\ 80?

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Alligation rule: to obtain a target mean price $M$ from prices $P_1$ and $P_2$, mix in the ratio $(P_2-M):(M-P_1)$.
Updated On: Jul 15, 2026
  • 2:1
  • 2:3
  • 1:2
  • 3:2
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The Correct Option is C

Approach Solution - 1

Step 1: Let the ratio of the Rs. 60 coffee to the Rs. 90 coffee be \( x:y \). The blended price is the weighted average, so \( \frac{60x+90y}{x+y}=80 \).

Step 2: Multiplying both sides by \( x+y \) gives \( 60x+90y=80x+80y \).

Step 3: Rearranging gives \( 90y-80y=80x-60x \), which simplifies to \( 10y=20x \), so \( \frac{x}{y}=\frac{1}{2} \).
\[ \boxed{1:2} \]
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Approach Solution -2

Let \( f \) be the fraction, by weight, of Rs. 60 coffee in the blend, so \( 1-f \) is the fraction of Rs. 90 coffee. The blended price is then \( 60f+90(1-f)=90-30f \). We can test each ratio option by converting it to a fraction \( f \) and checking whether \( 90-30f \) comes out to Rs. 80.

  1. 2:1: Here \( f=2/3 \), giving a blended price of \( 90-30 \times \tfrac{2}{3}=90-20=70 \), not Rs. 80.
  2. 2:3: Here \( f=2/5 \), giving a blended price of \( 90-30 \times 0.4=90-12=78 \), close to but not exactly Rs. 80.
  3. 1:2: Here \( f=1/3 \), giving a blended price of \( 90-30 \times \tfrac{1}{3}=90-10=80 \), matching exactly.
  4. 3:2: Here \( f=3/5 \), giving a blended price of \( 90-30 \times 0.6=90-18=72 \), not Rs. 80.

Only a Rs. 60 coffee fraction of one-third, that is a ratio of 1:2 with the Rs. 90 coffee, brings the blended price to exactly Rs. 80.

Therefore, the correct answer is 1:2.

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