Practice Questions
Concept Explanation
The alligation cross finds the ratio in which two ingredients at different prices must be mixed to obtain a desired mean price.
Key Formulas
- (Cheaper quantity) / (Dearer quantity) = (d − m) / (m − c)
- Where c = cheaper price, d = dearer price, m = mean price
- Draw the cross: link each price to the difference between mean and the other price
Example
Cheaper Rs. 20/kg, dearer Rs. 40/kg, mean Rs. 28/kg. Ratio = (40 − 28) : (28 − 20) = 12 : 8 = 3 : 2.
Common Trap
Cheaper quantity pairs with (dearer − mean), not (mean − cheaper) on the same side of the cross.
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Q1 Easy
Cheaper Rs. 20/kg, dearer Rs. 40/kg, mean Rs. 28/kg. Ratio cheaper : dearer is:
Explanation(40 − 28) : (28 − 20) = 12 : 8 = 3 : 2. -
Q2 Easy
Rs. 15/kg and Rs. 25/kg for mean Rs. 20/kg. Ratio is:
Explanation(25 − 20) : (20 − 15) = 5 : 5 = 1 : 1. -
Q3 Medium
Rs. 30/kg and Rs. 50/kg for mean Rs. 38/kg. Cheaper : dearer is:
Explanation(50 − 38) : (38 − 30) = 12 : 8 = 3 : 2. -
Q4 Easy
Alligation formula: cheaper/dearer ratio equals:
ExplanationCheaper : dearer = (d − m) : (m − c). -
Q5 Easy
Rs. 12/kg and Rs. 18/kg for Rs. 15/kg. Ratio cheaper : dearer is:
Explanation(18 − 15) : (15 − 12) = 3 : 3 = 1 : 1. -
Q6 Medium
Rs. 24/kg and Rs. 36/kg for Rs. 30/kg. Ratio is:
Explanation(36 − 30) : (30 − 24) = 6 : 6 = 1 : 1. -
Q7 Easy
Rs. 10/kg and Rs. 22/kg for Rs. 16/kg. Cheaper : dearer is:
Explanation(22 − 16) : (16 − 10) = 6 : 6 = 1 : 1.
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Q8 Hard
Ratio 3 : 2 at Rs. 20 and Rs. 35/kg gives mean:
ExplanationMean = (3×20 + 2×35)/5 = (60 + 70)/5 = Rs. 26/kg. -
Q9 Medium
Rs. 40/kg and Rs. 70/kg for Rs. 52/kg. Ratio cheaper : dearer is:
Explanation(70 − 52) : (52 − 40) = 18 : 12 = 3 : 2. -
Q10 Medium
Rs. 5/kg and Rs. 11/kg for Rs. 8/kg. Ratio cheaper : dearer is:
Explanation(11 − 8) : (8 − 5) = 3 : 3 = 1 : 1. -
Q11 Hard
30 kg mixture in ratio 2 : 3 from Rs. 18 and Rs. 33/kg. Mean is:
ExplanationMean = (2×18 + 3×33)/5 = (36 + 99)/5 = Rs. 27/kg. -
Q12 Medium
Rs. 16/kg and Rs. 28/kg for Rs. 22/kg. Cheaper share of total is:
ExplanationRatio = (28−22):(22−16) = 6:6 = 1:1. Cheaper share = 1/2. -
Q13 Easy
Rs. 50/kg and Rs. 80/kg for Rs. 65/kg. Ratio cheaper : dearer is:
Explanation(80 − 65) : (65 − 50) = 15 : 15 = 1 : 1. -
Q14 Easy
Which mean is possible from Rs. 20/kg and Rs. 50/kg?
ExplanationMean must lie between 20 and 50. Only Rs. 35/kg qualifies.
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DS1 Easy
What is the ratio of cheaper to dearer?
Statement ICheaper Rs. 20/kg, dearer Rs. 40/kg, mean Rs. 28/kg.
Statement IICheaper and dearer are mixed in ratio 3 : 2.
ExplanationEach gives ratio 3 : 2. -
DS2 Easy
Can alligation be applied?
Statement ITwo ingredients have different unit prices.
Statement IIA mean price between the two prices is required.
ExplanationNeed both prices and target mean to find ratio.
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DS3 Easy
Is the ratio 1 : 1?
Statement IRs. 15/kg and Rs. 25/kg give mean Rs. 20/kg.
Statement IIRs. 30/kg and Rs. 50/kg give mean Rs. 40/kg.
ExplanationEach gives ratio (d−m):(m−c) = 1 : 1. -
DS4 Easy
What is the mean price?
Statement IIngredients at Rs. 24/kg and Rs. 36/kg are mixed 1 : 1.
Statement IIRatio is 1 : 1 and prices are Rs. 24 and Rs. 36/kg.
ExplanationEach gives mean = (24 + 36)/2 = Rs. 30/kg.