Question:
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?
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
Use alligation. For a mean price of Rs.\ 80 from items priced at Rs.\ 60 and Rs.\ 90, the mixing ratio is inverse of deviations from the mean:
\[
\text{Ratio} = (90-80) : (80-60) = 10 : 20 = 1 : 2.
\]
So, coffee at Rs.\ 60 : coffee at Rs.\ 90 $= 1:2$.
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Approach Solution -2
Coffee priced at Rs. 60 and Rs. 90 must be mixed to get a blend priced at Rs. 80. We can test each ratio option by checking whether it gives a weighted average price of exactly Rs. 80.
- 2:1: Mixing 2 parts of Rs. 60 coffee with 1 part of Rs. 90 coffee gives \( \frac{2 \times 60+1 \times 90}{3}=\frac{120+90}{3}=70 \) Rs, not Rs. 80.
- 2:3: Mixing 2 parts of Rs. 60 coffee with 3 parts of Rs. 90 coffee gives \( \frac{2 \times 60+3 \times 90}{5}=\frac{120+270}{5}=78 \) Rs, close but not exactly Rs. 80.
- 1:2: Mixing 1 part of Rs. 60 coffee with 2 parts of Rs. 90 coffee gives \( \frac{1 \times 60+2 \times 90}{3}=\frac{60+180}{3}=80 \) Rs, matching exactly.
- 3:2: Mixing 3 parts of Rs. 60 coffee with 2 parts of Rs. 90 coffee gives \( \frac{3 \times 60+2 \times 90}{5}=\frac{180+180}{5}=72 \) Rs, not Rs. 80.
Only the ratio 1:2, one part of the Rs. 60 coffee to two parts of the Rs. 90 coffee, gives a blended price of exactly Rs. 80.
Therefore, the correct answer is 1:2.
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Approach Solution -3
Coffee priced at Rs. 60 is Rs. 20 below the target blended price of Rs. 80, a shortfall per kilogram, while coffee at Rs. 90 is Rs. 10 above it, a surplus per kilogram. For the blend to average exactly Rs. 80, the total shortfall contributed by the Rs. 60 coffee must exactly balance the total surplus contributed by the Rs. 90 coffee. We can test each ratio option by checking whether this balance holds.
- 2:1: Total shortfall \( =20 \times 2=40 \), total surplus \( =10 \times 1=10 \); these are not equal, so the blend would fall short of Rs. 80.
- 2:3: Total shortfall \( =20 \times 2=40 \), total surplus \( =10 \times 3=30 \); these are not equal either.
- 1:2: Total shortfall \( =20 \times 1=20 \), total surplus \( =10 \times 2=20 \); these balance exactly.
- 3:2: Total shortfall \( =20 \times 3=60 \), total surplus \( =10 \times 2=20 \); these are far from balanced.
Only the ratio 1:2 makes the shortfall from the cheaper coffee exactly balance the surplus from the costlier coffee, giving a blend priced at exactly Rs. 80.
Therefore, the correct answer is 1:2.
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