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CAT Ratio, Ages & Mixtures Questions
Practise ratio, ages & mixtures (quantitative aptitude) for the Common Admission Test: 10 multiple-choice questions, each with the correct answer and a worked explanation. Click an option to check it, or “New questions” for another set.
Ratio, Ages & Mixtures practice
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Q1.The present ages of two people are in the ratio 3:2. After 9 years the sum of their ages will be 38. What is the present age of the elder person?
Show answer & explanation
Answer: A — 12 years
Let ages be 3x and 2x. After 9 years: 3x + 9 + 2x + 9 = 38 → 5x = 20 → x = 4. Elder = 3×4 = 12 years.
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Q2.₹3,888 is divided between A and B in the ratio 5:1. What is B’s share?
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Answer: C — ₹648
Total parts = 5 + 1 = 6; one part = 3,888/6 = 648; second share = 1 × 648 = ₹648.
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Q3.In what ratio must rice at ₹70/kg be mixed with rice at ₹100/kg to get a mixture worth ₹80/kg?
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Answer: B — 2:1
Alligation: (dearer − mean) : (mean − cheaper) = (100 − 80) : (80 − 70) = 20:10 = 2:1.
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Q4.₹3,360 is divided between A and B in the ratio 1:6. What is B’s share?
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Answer: C — ₹2,880
Total parts = 1 + 6 = 7; one part = 3,360/7 = 480; second share = 6 × 480 = ₹2,880.
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Q5.₹1,548 is divided between A and B in the ratio 2:7. What is B’s share?
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Answer: D — ₹1,204
Total parts = 2 + 7 = 9; one part = 1,548/9 = 172; second share = 7 × 172 = ₹1,204.
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Q6.In what ratio must rice at ₹100/kg be mixed with rice at ₹150/kg to get a mixture worth ₹140/kg?
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Answer: C — 1:4
Alligation: (dearer − mean) : (mean − cheaper) = (150 − 140) : (140 − 100) = 10:40 = 1:4.
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Q7.The present ages of two people are in the ratio 5:2. After 6 years the sum of their ages will be 54. What is the present age of the elder person?
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Answer: C — 30 years
Let ages be 5x and 2x. After 6 years: 5x + 6 + 2x + 6 = 54 → 7x = 42 → x = 6. Elder = 5×6 = 30 years.
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Q8.In what ratio must rice at ₹120/kg be mixed with rice at ₹150/kg to get a mixture worth ₹130/kg?
Show answer & explanation
Answer: A — 2:1
Alligation: (dearer − mean) : (mean − cheaper) = (150 − 130) : (130 − 120) = 20:10 = 2:1.
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Q9.₹3,480 is divided between A and B in the ratio 3:3. What is B’s share?
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Answer: D — ₹1,740
Total parts = 3 + 3 = 6; one part = 3,480/6 = 580; second share = 3 × 580 = ₹1,740.
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Q10.₹2,475 is divided between A and B in the ratio 5:6. What is B’s share?
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Answer: B — ₹1,350
Total parts = 5 + 6 = 11; one part = 2,475/11 = 225; second share = 6 × 225 = ₹1,350.
How to approach ratio, ages & mixtures questions
Write the ratio as parts (e.g. 3:5 → 8 parts), find the value of one part, then scale. For mixtures, alligation gives the ratio as (dearer − mean) : (mean − cheaper).
About CAT
Common Admission Test — conducted by Indian Institutes of Management (convening IIM rotates). The entrance exam for IIM MBA programmes, with VARC, DILR and Quantitative Ability sections.
Original practice questions written for this site in the style and difficulty of each exam’s syllabus. They are not past papers and the site is not affiliated with any exam body. Exam patterns, marking schemes and syllabi change — always check the latest official notification.
CAT practice topics
| Topic | Section | Question source |
|---|---|---|
| Percentages | Quantitative aptitude | Calculated (new numbers every set) |
| Ratio, Ages & Mixtures | Quantitative aptitude | Calculated (new numbers every set) |
| Time, Work & Pipes | Quantitative aptitude | Calculated (new numbers every set) |
| Algebra | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |
| Data Interpretation | Data interpretation | Calculated (new numbers every set) |
| Verbal Reasoning & Analogies | Reasoning | Calculated + question bank |