Ratio and proportion questions, with answers
Ratio and proportion is the aptitude topic that hides inside the others — mixtures, partnerships, ages, time and work all reduce to it — so a weak grip here costs marks across the whole paper. The method is one move: replace the ratio with actual numbers by introducing a multiplier, then let the question's condition fix the multiplier.
Here are the question shapes with that move worked through. Then take the free Aptitude diagnostic — ten questions across the seventeen aptitude topics, and a clear picture of which ones need work before the next test.
The questions, with answers
1.What is the difference between a ratio and a proportion?
A ratio compares two quantities of the same kind: 3 : 5 says the first is three-fifths of the second, and it has no units. A proportion is a statement that two ratios are equal: a : b = c : d, read "a is to b as c is to d". The working rule is cross-multiplication — if a : b = c : d then a × d = b × c — and it is what lets you solve for a missing term. If 4 : 6 = x : 15, then 6x = 60 and x = 10. The outer terms a and d are the extremes, the inner terms b and c the means, and the product of the means equals the product of the extremes.
2.How do you divide an amount in a given ratio?
Add the parts, find the value of one part, multiply. To divide Rs 2,700 among three people in the ratio 2 : 3 : 4, the total is 2 + 3 + 4 = 9 parts, one part is 2700 / 9 = 300, so the shares are 600, 900 and 1,200. Check that they sum to the total. A variant gives a difference instead: if the shares are in 2 : 3 : 4 and the largest exceeds the smallest by Rs 500, then 4 - 2 = 2 parts equal 500, one part is 250, and the total is 9 × 250 = Rs 2,250.
3.How do you combine two ratios that share a term, like A : B and B : C?
Make the shared term the same number in both. If A : B = 2 : 3 and B : C = 4 : 5, B is 3 in one ratio and 4 in the other; scale to their LCM, 12. Multiply the first ratio by 4 to get A : B = 8 : 12, and the second by 3 to get B : C = 12 : 15. Then A : B : C = 8 : 12 : 15. The result is not 2 : 3 : 5 — writing the ratios side by side without matching the middle term is the standard error. With three ratios, match one pair at a time.
4.How do you solve a problem where the ratio changes after some people join or leave?
Introduce a multiplier for the original ratio, apply the change, and set up the new ratio as an equation. Two people's ages are in the ratio 3 : 4; in five years the ratio will be 4 : 5. Let the ages be 3k and 4k. Then (3k + 5) / (4k + 5) = 4 / 5, so 15k + 25 = 16k + 20 and k = 5: the ages are 15 and 20. Check: in five years, 20 and 25, which is 4 : 5. The same setup handles "6 more girls join" or "Rs 200 is removed from each" — change the actual quantities, not the ratio numbers.
5.What are direct and inverse proportion, and how do you tell which applies?
Two quantities are in direct proportion when they rise and fall together in the same factor — twice the pens, twice the cost — so their ratio stays constant: x / y is fixed. They are in inverse proportion when one rises as the other falls in the same factor — twice the workers, half the days — so their product stays constant: x × y is fixed. The test is to ask what happens when one quantity doubles. If 8 workers take 15 days, 12 workers take 8 × 15 / 12 = 10 days (inverse). If 5 pens cost Rs 60, 8 pens cost 60 × 8 / 5 = Rs 96 (direct). Choosing the wrong one flips the answer, so name the type before you calculate.
6.How are profits shared in a partnership when investments run for different periods?
In the ratio of capital multiplied by time, because a rupee invested for a year has earned more than a rupee invested for a month. A invests Rs 20,000 for 12 months and B invests Rs 30,000 for 8 months. Their capital-months are 240,000 and 240,000, so they share the profit equally despite B having put in more money. If A had stayed the full year and B had joined after four months, B's time is 8 months, and the ratio is 20 × 12 : 30 × 8 = 240 : 240 — the same calculation. When a partner withdraws or adds money mid-year, split their investment into periods and add the products.
7.What are the mean proportional and the third proportional?
The mean proportional between a and b is the number x with a : x = x : b, so x² = ab and x = √(ab): between 4 and 9 it is 6, since 4 : 6 = 6 : 9. The third proportional to a and b is the number x with a : b = b : x, so x = b² / a: the third proportional to 4 and 6 is 36 / 4 = 9. The fourth proportional to a, b and c is the x with a : b = c : x, so x = bc / a. Interviewers also use duplicate ratio — the ratio of the squares, so the duplicate of 2 : 3 is 4 : 9 — and sub-duplicate, the ratio of the square roots.
8.How do you solve a coins-in-a-ratio problem?
Convert the count ratio into a value ratio before using the total. A bag has 1-rupee, 2-rupee and 5-rupee coins in the ratio 3 : 2 : 1 and holds Rs 240 in all. With 3k, 2k and k coins, the value is 3k × 1 + 2k × 2 + k × 5 = 12k rupees. So 12k = 240, k = 20, and there are 60, 40 and 20 coins. The trap is dividing 240 in the ratio 3 : 2 : 1 directly, which would split the money, not the coins. Whenever the ratio counts objects of different values, multiply each count by its value first; whenever it already describes money, divide directly.
How the diagnostic asks it
One question from the Aptitude bank, exactly as a sitting would show it. The bank has 4 on ratio & proportion and 60 across Aptitude.
Divide Rs. 3600 between A and B in the ratio 5:4. What is B's share?
- 1Rs. 1440
- 2Rs. 2000
- 3Rs. 1800
- 4Rs. 1600correct
Total parts = 5+4 = 9. Value of one part = 3600/9 = 400. B's share = 4 x 400 = Rs. 1600.
Measure it
Reading answers tells you what’s true. A diagnostic tells you what you get wrong.
10 Aptitude questions across its topics, easy to hard, about fifteen minutes. You get a readiness figure with the arithmetic shown, the topics you missed named, and a practice set sized for today. Free: 1 diagnostic a month and 15 problems a day. No card.