Ratio, Proportion & Ages MCQs With Answers
If two quantities are compared, a ratio question is never far away. These ratio, proportion and ages MCQs cover simplifying ratios, dividing an amount in a given ratio, compound ratios such as a:b:c, third, fourth and mean proportionals, mixtures and alligation, boys and girls in a class, and present and future ages of fathers, sons and friends. They help candidates preparing for PPSC, FPSC, NTS, CSS screening and other competitive exams.
Take a scored quiz instead →If A : B = 2 : 3 and B : C = 4 : 5, what is A : B : C?
Make the common term B equal in both ratios. The LCM of 3 and 4 is 12: A : B = 8 : 12 and B : C = 12 : 15.
So A : B : C = 8 : 12 : 15.
The ratio of two numbers is 5:6 and their LCM is 150. What is the larger number?
5x and 6x. LCM = 30x = 150 => x=5. Larger = 6*5=30.
The sum of the ages of a father and son is 50. If the father is 4 times as old as the son, how old is the son?
x + 4x = 50 => 5x = 50 => x = 10.
The ratio of ages of A and B is 3:4 and the sum of their ages is 42. What is the age of A?
3x+4x=42 => 7x=42 => x=6. A = 3*6 = 18.
The ratio of two numbers is 3:5 and their sum is 80. What is the smaller number?
3x+5x=80 => 8x=80 => x=10. Smaller number = 3*10=30.
The sum of three numbers is 98. If the ratio of the first to the second is 2:3 and the ratio of the second to the third is 5:8, find the second number.
Ratio a:b=2:3, b:c=5:8 => a:b:c = 10:15:24. Sum of parts = 49. 49 parts = 98 => 1 part = 2. Second number = 15 * 2 = 30.
The ratio of 25 minutes to 1 hour is:
25:60 = 5:12.
A trader mixes 20kg rice @ 10/kg and 30kg rice @ 15/kg. What is the avg price?
(200+450)/50 = 650/50 = 13.
If a:b = 3:4 and b:c = 5:6, then a:c is:
a/c = (a/b)*(b/c) = (3/4)*(5/6) = 15/24 = 5/8.
The sum of ages of A and B is 30. A is 4 years older than B. How old is B?
B+(B+4)=30 => 2B=26 => B=13.
The ratio of boys to girls in a class is 2:3. If there are 20 boys, how many girls?
2 units = 20, 1 unit = 10. 3 units = 30.
Two numbers in ratio 3:4, sum 70. Find larger.
7 parts = 70. 1 part = 10. Larger=4*10=40.
a:b=1:2, b:c=2:3. a:c?
a/c = 1/2 * 2/3 = 1/3.
A mixture of milk and water is in ratio 3:2. If there are 30 liters in total, how much water must be added to make the ratio 2:3?
Initial: Milk=18, Water=12. New ratio 2:3 => Milk/Water_new = 2/3. 18/W_new = 2/3 => W_new = 27. Water added = 27 - 12 = 15L.
Two numbers are in ratio 5:6. If their sum is 121, find the larger number.
11 parts = 121. 1 part = 11. Larger = 6 * 11 = 66.
Ratio a:b = 2:3, b:c = 4:5. a:b:c is:
a:b=8:12, b:c=12:15. So 8:12:15.
Ratio of boys and girls is 4:5. Total students = 45. Number of girls?
4+5=9 parts = 45. 1 part = 5. Girls = 5*5 = 25.
a:b = 3:4, b:c = 8:9. a:c?
a/c = 3/4 * 8/9 = 24/36 = 2/3.
Angle of a triangle are in ratio 1:2:3. What is the largest angle?
1x + 2x + 3x = 180 => 6x = 180 => x = 30. Angles are 30, 60, 90.
The ratio of boys and girls in a class is 3:2. If there are 30 boys, how many girls?
3x = 30 => x = 10. Girls = 2x = 20.
If a:b = 2:3 and b:c = 4:5, find a:c.
a/c = (a/b)*(b/c) = 2/3 * 4/5 = 8/15.
The ratio of two numbers is 5:7 and their sum is 72. Find the numbers.
12x = 72 => x = 6. 5*6=30, 7*6=42.
If a:b = 1:2 and b:c = 3:4, find a:b:c.
a:b = 3:6, b:c = 6:8. a:b:c = 3:6:8.
The LCM of two numbers is 48 and the ratio of the numbers is 2:3. Find the sum of the numbers.
Numbers are 2x and 3x. LCM is 6x. 6x = 48 => x = 8. Numbers are 16 and 24. Sum = 16 + 24 = 40.
The ratio of two numbers is 3:4 and their HCF is 5. Find the numbers.
- When the HCF is 5, the numbers must be 3 × 5 and 4 × 5, which gives 15 and 20.
- Both conditions check out: 15 : 20 reduces to 3 : 4, and the HCF of 15 and 20 is 5.
- Option A 10, 15 has the ratio 2 : 3, so it fails the ratio condition.
- Option C 20, 25 has an HCF of 5 but a ratio of 4 : 5, so it fails the other condition.
- General pattern: two numbers in the ratio a : b with HCF h are always ah and bh.
- Ratio and HCF questions in PPSC and NTS papers usually come down to this single substitution.
The sum of two numbers is 40 and their difference is 10. Find the ratio of the two numbers.
Let numbers be x and y. x + y = 40, x - y = 10. Adding: 2x = 50 => x = 25. y = 15. Ratio = 25 : 15 = 5 : 3.
If a:b = 3:5 and b:c = 10:9, find a:b:c.
Multiply a:b by 2 to equate b: a:b = 6:10. So a:b:c = 6 : 10 : 9.
Present ages of father and son are in ratio 7:2. After 10 years, ratio will be 9:4. What is the father’s present age?
(7x + 10) / (2x + 10) = 9 / 4 => 4(7x + 10) = 9(2x + 10) => 28x + 40 = 18x + 90 => 10x = 50 => x = 5. Father's age = 7 * 5 = 35 years.
If A:B = 3:4, B:C = 8:9, and C:D = 15:16, find A:D.
A/D = (A/B) * (B/C) * (C/D) = (3/4) * (8/9) * (15/16) = (3 * 8 * 15) / (4 * 9 * 16) = 360 / 576 = 5 / 8.
The ratio of present ages of A and B is 4:5. After 5 years, the ratio becomes 5:6. What is A’s present age?
Let ages be 4x and 5x. (4x + 5)/(5x + 5) = 5/6 => 6(4x + 5) = 5(5x + 5) => 24x + 30 = 25x + 25 => x = 5. A's age = 4 * 5 = 20 years.
If a:b = 2:3, b:c = 4:5, and c:d = 6:7, find a:d.
a/d = (a/b) * (b/c) * (c/d) = (2/3) * (4/5) * (6/7) = 48 / 105 = 16 / 35.
Two numbers are 20% and 50% more than a third number respectively. What is the ratio of the two numbers?
Let third number = 100. First = 120, Second = 150. Ratio = 120 : 150 = 4 : 5.
The ratio of two numbers is 4:5 and their HCF is 12. What is their LCM?
Let the numbers be 4x and 5x where x is HCF = 12. The numbers are 48 and 60. LCM = 4 * 5 * 12 = 240.
The sum of ages of a father and his son is 45 years. Five years ago, the product of their ages was 124. How old is the father now?
Let father's age = F and son's age = S. F + S = 45. Five years ago: (F - 5)(S - 5) = 124. Since S = 45 - F, (F - 5)(40 - F) = 124 => F^2 - 45F + 324 = 0 => (F - 36)(F - 9) = 0. Father's age is 36 years.
If 40% of a number is equal to two-thirds of another number, what is the ratio of the first number to the second number?
Let numbers be A and B. 0.40 * A = (2/3) * B => (2/5) * A = (2/3) * B => A / B = (2/3) / (2/5) = 5 / 3. Ratio = 5 : 3.
The base and height of a triangle are in the ratio 3:2 and its area is 108 cm². Find its height.
Let base = 3x, height = 2x. Area = 0.5 * base * height = 0.5 * (3x) * (2x) = 3x^2. 3x^2 = 108 => x^2 = 36 => x = 6. Height = 2 * 6 = 12 cm.
The ratio of the ages of two persons A and B is 3:4. Six years ago, the ratio was 2:3. What is B’s present age?
Let present ages be 3x and 4x. (3x - 6) / (4x - 6) = 2 / 3 => 3(3x - 6) = 2(4x - 6) => 9x - 18 = 8x - 12 => x = 6. B's age = 4 * 6 = 24 years.
If 4A = 5B = 6C, what is the ratio A:B:C?
Divide by LCM of 4, 5, 6 (which is 60): 4A/60 = 5B/60 = 6C/60 => A/15 = B/12 = C/10. So A:B:C = 15:12:10.
The present age ratio of father and son is 7:2. After 15 years, the ratio becomes 2:1. What is the present age of the father?
Let present ages be 7x and 2x. (7x + 15) / (2x + 15) = 2 / 1 => 7x + 15 = 4x + 30 => 3x = 15 => x = 5. Present age of father = 7 * 5 = 35 years.
If x:y = 3:2 and y:z = 5:4, what is the value of x:z?
- Multiply the two ratios as fractions: x/z = (x/y) × (y/z) = (3/2) × (5/4) = 15/8, so x:z = 15:8.
- The y terms cancel out, and that is why chaining ratios in this way works.
- A second route is to make y equal in both ratios. Scale 3:2 to 15:10 and 5:4 to 10:8, giving x:y:z = 15:10:8.
- Option B 8:15 is the reversed ratio z:x, so always check the order of the letters before answering.
- Because 15/8 is 1.875, the ratio also tells you that x is nearly twice the size of z.
What is the fourth proportional to 4, 9, and 12?
- The fourth proportional to a, b and c satisfies a : b = c : x, so here 4 : 9 = 12 : x.
- Cross multiply to solve: 4x = 9 × 12 = 108, so x = 108 ÷ 4 = 27.
- In short form the answer is x = (b × c) ÷ a, which is worth memorising.
- Check the pattern: 4 grows to 9 by a factor of 2.25, and 12 grows to 27 by the same 2.25.
- Do not confuse this with the third proportional, where the middle term repeats as a : b = b : x.
- Option D 36 comes from multiplying 12 by 3, which ignores the 9 : 4 relationship in the question.
If 30% of (A + B) = 50% of (A – B), find the ratio A:B.
0.3(A + B) = 0.5(A - B) => 3A + 3B = 5A - 5B => 2A = 8B => A = 4B => A:B = 4:1.
The ratio of two numbers is 3:5 and their HCF is 12. What is their LCM?
The numbers are 3 * 12 = 36 and 5 * 12 = 60. LCM = HCF * product of coprime ratios = 12 * 3 * 5 = 180.
In a mixture of 60 liters, the ratio of milk to water is 2:1. How much water should be added to make the ratio 1:2?
Initial Milk = 40L, Water = 20L. To make ratio 1:2 (Milk:Water = 40:Water_new) => Water_new = 80L. Added water = 80 - 20 = 60 liters.
If a:b = 3:4 and b:c = 8:9, what is a:b:c?
To equalize b: multiply a:b by 2 => a:b = 6:8. Since b:c = 8:9, a:b:c = 6:8:9.
What is the third proportional to 9 and 18?
Third proportional c satisfies 9:18 = 18:c => 9c = 324 => c = 36.
If 15% of x is equal to 20% of y, what is the ratio x:y?
0.15x = 0.20y => x/y = 0.20 / 0.15 = 20 / 15 = 4 / 3. So x:y = 4:3.
The sum of ages of father and son is 50 years. Five years ago, father was 7 times as old as son. What is father’s present age?
Let father = F, son = S. F + S = 50. Five years ago: (F - 5) = 7(S - 5) => F - 5 = 7S - 35 => F = 7S - 30. Substitute: 7S - 30 + S = 50 => 8S = 80 => S = 10. F = 40 years.
If the ratio of two numbers is 4:7 and their sum is 132, find the smaller number.
Let numbers be 4x and 7x. 4x + 7x = 132 => 11x = 132 => x = 12. Smaller number = 4 * 12 = 48.
What is the fourth proportional to 3, 7, and 12?
Let fourth proportional be x. 3 : 7 :: 12 : x => 3/7 = 12/x => 3x = 84 => x = 28.
In what ratio must water be mixed with milk costing Rs. 12 per liter to get a mixture worth Rs. 9 per liter?
Using alligation rule: (Cost of Milk - Mean Price) : (Mean Price - Cost of Water) = (12 - 9) : (9 - 0) = 3 : 9 = 1 : 3.
The ratio of boys to girls in a school is 5:3. If there are 120 girls, how many boys are in the school?
Let ratio unit be x. 3x = 120 => x = 40. Number of boys = 5x = 5 * 40 = 200.
The present ages of father and son are in the ratio 7:2. If the father is 30 years older than the son, what is the son’s age?
7x - 2x = 30 => 5x = 30 => x = 6. Son's age = 2x = 2 * 6 = 12 years.
What is the third proportional to 4 and 12?
If c is third proportional to a and b, then a:b = b:c => 4/12 = 12/c => 4c = 144 => c = 36.
If the ratio of two numbers is 3:4 and their HCF is 5, what is their LCM?
Numbers are 3*5 = 15 and 4*5 = 20. LCM of 15 and 20 is 60.
The ratio of two numbers is 4:7 and their sum is 132. What is the difference between the two numbers?
Let the numbers be 4x and 7x. 4x + 7x = 11x = 132 => x = 12. The difference is 7x - 4x = 3x = 3 * 12 = 36.
Present ages of A and B are in ratio 3:4. After 5 years, the ratio becomes 4:5. What is A’s present age?
Let ages be 3x and 4x. (3x + 5)/(4x + 5) = 4/5 => 5(3x + 5) = 4(4x + 5) => 15x + 25 = 16x + 20 => x = 5. A's age = 3x = 15 years.
Two numbers are in the ratio 5:8. If 4 is added to each number, the ratio becomes 2:3. What is the smaller number?
(5x + 4)/(8x + 4) = 2/3 => 3(5x + 4) = 2(8x + 4) => 15x + 12 = 16x + 8 => x = 4. Smaller number = 5x = 5 * 4 = 20.
If 1/4 of a number is equal to 1/3 of another number, what is the ratio of the first number to the second number?
(1/4)A = (1/3)B => A/B = 4/3 => Ratio is 4:3.
The ratio of two numbers is 3:5. If their sum is 160, what is the value of the larger number?
Let the numbers be 3x and 5x. Their sum = 3x + 5x = 8x = 160. So x = 20. The larger number is 5x = 5 × 20 = 100.
Divide Rs. 1200 between A and B in the ratio 3:5. What is B’s share?
Total parts = 3 + 5 = 8. B's share = (5 / 8) * 1200 = 5 * 150 = Rs. 750.
The length and breadth of a rectangular field are in ratio 4:3. If the perimeter is 140 m, find its length.
Perimeter = 2(4x + 3x) = 14x = 140 => x = 10. Length = 4x = 4 * 10 = 40 m.
The present age of a mother is 3 times that of her daughter. 10 years ago, she was 5 times as old as her daughter. Find daughter’s present age.
Let daughter's age = x, mother's = 3x. 10 years ago: 3x - 10 = 5(x - 10) => 3x - 10 = 5x - 50 => 2x = 40 => x = 20 years.
A man is 24 years older than his son. In 2 years, his age will be twice the age of his son. Present age of son is:
Let son's age = x, man's age = x + 24. In 2 years: (x + 24) + 2 = 2(x + 2) => x + 26 = 2x + 4 => x = 22 years.
If the ratio of two numbers is 3:4 and their sum is 84, find the larger number.
Total parts = 3 + 4 = 7 parts. Value per part = 84 / 7 = 12. The larger number corresponds to 4 parts, so 4 * 12 = 48.
A father is 4 times as old as his son. In 20 years, he will be twice as old as his son. How old is the son now?
Let son's age = x, father's age = 4x. In 20 years: 4x + 20 = 2(x + 20) => 4x + 20 = 2x + 40 => 2x = 20 => x = 10 years.
Present ages of A and B are in ratio 5:6. After 5 years, the ratio becomes 6:7. What is A’s present age?
Let present ages be 5x and 6x. Equation: (5x + 5)/(6x + 5) = 6/7 => 35x + 35 = 36x + 30 => x = 5. A's age = 5 * 5 = 25 years.