Ratio and proportion is the base for several other aptitude topics, so it appears in almost every placement test, bank exam and SSC paper. This set covers ratios and proportions, mixtures and alligation, problems on ages and partnership, with a short worked solution for every question.
How to practise: read each question and tap the option you think is correct. You will see right away whether you got it, along with a short explanation, and your score is tracked at the bottom of the screen. This set has 15 questions.
Topics covered in this set
- Combining ratios and dividing an amount in a ratio
- Mean and fourth proportional
- Mixtures and the rule of alligation
- Repeated replacement in a mixture
- Problems on ages
- Simple and compound partnership
Aptitude MCQs with answers and explanations
Q1. If A : B = 2 : 3 and B : C = 4 : 5, what is A : B : C?
a) 8 : 12 : 16
b) 6 : 9 : 10
c) 8 : 12 : 15
d) 2 : 3 : 5
Q2. Rs 1,200 is divided between two people in the ratio 3 : 5. What is the larger share?
a) Rs 750
b) Rs 720
c) Rs 800
d) Rs 450
Q3. What is the mean proportional between 9 and 16?
a) 14
b) 25
c) 10
d) 12
Q4. What is the fourth proportional to 4, 9 and 12?
a) 18
b) 27
c) 24
d) 36
Q5. Two numbers are in the ratio 3 : 4. If 6 is added to each, the ratio becomes 4 : 5. What are the numbers?
a) 12 and 16
b) 18 and 24
c) 15 and 20
d) 21 and 28
Q6. In what ratio must rice costing Rs 40 per kg be mixed with rice costing Rs 55 per kg to get a mixture worth Rs 45 per kg?
a) 3 : 2
b) 2 : 3
c) 1 : 2
d) 2 : 1
Q7. A 60-litre mixture has milk and water in the ratio 2 : 1. How much water must be added to make the ratio 1 : 1?
a) 20 litres
b) 30 litres
c) 10 litres
d) 15 litres
Q8. A container has 40 litres of milk. 4 litres are taken out and replaced with water, and this is done twice in total. How much milk is left?
a) 36 litres
b) 32 litres
c) 32.4 litres
d) 33.6 litres
Q9. A father is three times as old as his son. After 10 years, he will be twice as old as his son. What is the son's present age?
a) 12 years
b) 15 years
c) 8 years
d) 10 years
Q10. The sum of the present ages of A and B is 50 years. Five years ago their ages were in the ratio 3 : 2. What is B's present age?
a) 21 years
b) 24 years
c) 25 years
d) 20 years
Q11. The present ages of two brothers are in the ratio 4 : 5. After 6 years the ratio will be 5 : 6. What is the elder brother's present age?
a) 36 years
b) 25 years
c) 30 years
d) 24 years
Q12. A invests Rs 20,000 for 12 months and B invests Rs 30,000 for 8 months. In what ratio should they share the profit?
a) 2 : 3
b) 1 : 1
c) 3 : 2
d) 4 : 3
Q13. A, B and C invest Rs 5,000, Rs 7,000 and Rs 8,000 for the same period. Out of a profit of Rs 4,000, what is C's share?
a) Rs 1,600
b) Rs 1,000
c) Rs 1,800
d) Rs 1,400
Q14. A starts a business with Rs 45,000. B joins after 3 months with Rs 60,000. Out of a year-end profit of Rs 28,000, what is B's share?
a) Rs 16,000
b) Rs 15,000
c) Rs 12,000
d) Rs 14,000
Q15. If x : y = 3 : 4, what is (4x + 5y) : (5x - 2y)?
a) 31 : 7
b) 32 : 9
c) 32 : 7
d) 7 : 32
Quick revision notes
- To combine A : B and B : C, make the common term B equal in both ratios.
- Mean proportional of a and b = square root of ab; fourth proportional of a, b, c = bc/a.
- Alligation: cheaper : dearer = (dearer price - mean price) : (mean price - cheaper price).
- Repeated replacement: quantity left = original x (1 - removed/total)^n.
- Ages: write both conditions as equations in one variable and solve.
- Partnership: share profit in the ratio of capital x time.
Frequently asked questions
What is the rule of alligation?
It finds the ratio in which two ingredients at different prices must be mixed to get a mixture at a given price. Subtract the mean price from the dearer price and the cheaper price from the mean price, and the two results give the ratio.
How do I solve age problems faster?
Use the ratio directly. Take the present ages as multiples of x, add or subtract the same number of years for both people, and form a single equation. Checking the answer options can also save time.
Is partnership profit always shared in the ratio of capital?
Only when everyone invests for the same time. If the time differs, multiply each person's capital by the number of months it was invested and share the profit in that ratio.
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