Q1. The ratio of 15 to 25 is
(a) 3:5
(b) 5:3
(c) 1:2
(d) 15:25
Answer: (a) Explanation: Divide both numbers by their HCF (5): 15÷5=3, 25÷5=5 → 3:5.
Q2. If 4 : 7 = x : 21, then x equals
(a) 12
(b) 28
(c) 21 (d) 4
Answer: (a)
Explanation: Cross‑multiply: 4×21 = 7x → 84 = 7x → x = 12.
Q3. The ratio of the ages of A and B is 2 : 3. If the sum of their ages is 50 years, the age of B is
(a) 20
(b) 30
(c) 25
(d) 15 Answer: (b)
Explanation: Total parts = 2+3 =5. One part = 50/5 =10. B = 3 parts =3×10 =30.
Q4. In a mixture, milk and water are in the ratio 3 : 2. If there are 18 litres of milk, the quantity of water is
(a) 12 litres
(b) 9 litres
(c) 6 litres
(d) 15 litres
Answer: (a) Explanation: 3 parts =18 L → 1 part =6 L. Water =2 parts =2×6 =12 L.
Q5. Which of the following ratios is equivalent to 5 : 9? (a) 10 : 18
(b) 15 : 27
(c) 20 : 36
(d) All of the above
Answer: (d)
Explanation: Multiplying 5:9 by 2, 3, and 4 gives the three listed ratios, all equivalent.
Q6. If a:b = 4:5 and b:c = 3:2, then a:c is
(a) 12:10
(b) 6:5
(c) 8:5
(d) 2:1
Answer: (b)
Explanation: Make b common: a:b =4:5 → multiply by 3 →12:15; b:c =3:2 → multiply by5 →15:10. Hence a:c =12:10 =6:5.
Q7. The fourth proportional to 2, 3, and 8 is
(a) 6
(b) 12
(c) 16
(d) 24 Answer: (b)
Explanation: For a:b = c:d → 2:3 = 8:d → 2d = 24 → d =12.
Q8. If 7 kg of rice costs ₹ 140, the cost of 15 kg of rice is
(a) ₹ 210
(b) ₹ 300
(c) ₹ 350
(d) ₹ 420
Answer: (b)
Explanation: Cost per kg =140/7 =₹20. For 15 kg → 15×20 =₹300.
Q9. The ratio of boys to girls in a class is 3 : 4. If there are 21 boys, the total number of students is
(a) 28
(b) 35
(c) 42
(d) 49
Answer: (c)
Explanation: 3 parts =21 → 1 part =7. Girls =4 parts =28. Total =21+28 =49? Wait compute: Actually total parts =3+4=7 → 1 part =21/3 =7 → total =7×7 =49. Oops check: 3 parts =21 → 1 part =7 → girls =4×7=28 → total =21+28=49. So answer is 49, option (d). Let’s correct.
Answer: (d)
Explanation: 3 parts =21 → 1 part =7. Girls =4×7=28. Total =21+28=49.
Q10. Two numbers are in the ratio 5 : 7. If their difference is 12, the larger number is
(a) 30
(b) 35
(c) 42
(d) 49 Answer: (c)
Explanation: Let numbers be 5x and 7x. Difference =7x-5x=2x=12 → x=6. Larger =7x=42.
Q11. If x : y = 2 : 3 and y : z = 4 : 5, then x : z is (a) 8:15
(b) 6:10
(c) 5:8
(d) 3:5
Answer: (a) Explanation: Make y common: x:y =2:3 → multiply by4 →8:12. y:z =4:5 → multiply by3 →12:15. Thus x:z =8:15.
Q12. A sum of ₹ 840 is divided among A, B, C in the ratio 2 : 3 : 5. The share of B is (a) ₹ 168
(b) ₹ 252
(c) ₹ 336
(d) ₹ 420
Answer: (b)
Explanation: Total parts =2+3+5=10. One part =840/10=84. B’s share =3 parts =3×84=252.
Q13. In a school, the ratio of teachers to students is 1 : 20. If there are 15 teachers, the number of students is
(a) 300
(b) 200 (c) 250
(d) 350
Answer: (a)
Explanation: 1 part =15 teachers → students =20 parts =20×15=300.
Q14. If a : b = 3 : 4 and b : c = 5 : 6, then a : b : c is
(a) 15:20:24 (b) 9:12:15
(c) 6:8:10
(d) 3:4:6
Answer: (a)
Explanation: Make b common: a:b =3:4 → multiply by5 →15:20. b:c =5:6 → multiply by4 →20:24. Combine →15:20:24.
Q15. The ratio of the speeds of two trains is 4 : 5. If the slower train covers 200 km in 5 hours, the distance covered by the faster train in the same time is (a) 250 km
(b) 240 km
(c) 260 km
(d) 300 km
Answer: (a)
Explanation: Speed ratio 4:5 → slower speed =200/5=40 km/h. Faster speed = (5/4)×40 =50 km/h. In 5h distance =50×5=250 km.
Q16. If 3 : 5 = x : 25, then x equals
(a) 15
(b) 10
(c) 5
(d) 20
Answer: (a)
Explanation: 3/5 = x/25 → cross‑multiply: 3×25 =5x →75=5x → x=15.
Q17. The ratio of the length to breadth of a rectangle is 7 : 3. If its perimeter is 80 cm, the length is
(a) 28 cm
(b) 21 cm
(c) 35 cm
(d) 14 cm
Answer: (a) Explanation: Let length=7x, breadth=3x. Perimeter =2(7x+3x)=20x=80 → x=4. Length=7×4=28 cm.
Q18. A mixture contains alcohol and water in the ratio 2 : 3. If 10 litres of water is added, the ratio becomes 2 : 5. The original quantity of alcohol is
(a) 4 litres
(b) 6 litres
(c) 8 litres
(d) 10 litres Answer: (c)
Explanation: Let alcohol=2x, water=3x. After adding 10 L water: water=3x+10. New ratio 2:5 → (2x)/(3x+10)=2/5 → cross‑multiply:10x=6x+20 →4x=20 →x=5. Alcohol=2x=10 L? Wait compute: 2x =25=10 L. But check options: 10 L is option (d). Let’s re-evaluate: Original ratio 2:3. After adding water, ratio becomes 2:5. So alcohol part unchanged. Equation: (2x)/(3x+10)=2/5 → cross multiply: 52x =2*(3x+10) →10x =6x+20 →4x=20 →x=5. Alcohol =2x=10 L. So answer should be (d) 10 litres. Let’s correct.
Answer: (d)
Explanation: Let alcohol=2x, water=3x. After adding 10 L water: (2x)/(3x+10)=2/5 → solving gives x=5 → alcohol=2×5=10 L.
Q19. If a : b = 5 : 6 and b : c = 9 : 10, then a : c is
(a) 3:4
(b) 15:20
(c) 3:4 (same as a)
(d) 5:12
Answer: (a)
Explanation: Make b common: a:b =5:6 → multiply by3 →15:18. b:c =9:10 → multiply by2 →18:20. Hence a:c =15:20 =3:4.
Q20. The ratio of the number of boys to girls in a school is 4 : 5. If there are 180 girls, the number of boys is
(a) 144
(b) 150
(c) 160
(d) 200
Answer: (a)
Explanation: 5 parts =180 → 1 part =36. Boys =4 parts =4×36=144.
Q21. A sum of money is divided among P, Q, R in the ratio 2 : 3 : 5. If Q gets ₹ 300, the total amount is
(a) ₹ 500
(b) ₹ 800
(c) ₹ 1000
(d) ₹ 1200
Answer: (c)
Explanation: Q’s share =3 parts =₹300 → 1 part =₹100. Total parts =2+3+5=10 → total =10×100=₹1000.
Q22. If x : y = 7 : 9 and y : z = 3 : 5, then x : z is
(a) 7:15
(b) 21:45
(c) 7:5
(d) 21:35
Answer: (a)
Explanation: Make y common: x:y =7:9 → multiply by? To match y=9 with y:z =3:5 multiply y:z by3 →9:15. So x:z =7:15.
Q23. In a bag, the ratio of red to blue marbles is 3 : 7. If there are 42 blue marbles, the number of red marbles is
(a) 12 (b) 18
(c) 21
(d) 24
Answer: (b)
Explanation: 7 parts =42 → 1 part =6. Red =3 parts =3×6=18.
Q24. Two numbers are in the ratio 8 : 11. If their sum is 190, the smaller number is
(a) 80
(b) 88
(c) 96
(d) 104
Answer: (a)
Explanation: Total parts =8+11=19 → 1 part =190/19=10. Smaller =8 parts =8×10=80.
Q25. If a : b = 2 : 3 and b : c = 4 : 5, then a : b : c is
(a) 8:12:15
(b) 6:9:10
(c) 4:6:5
(d) 2:3:5
Answer: (a)
Explanation: Make b common: a:b =2:3 → multiply by4 →8:12. b:c =4:5 → multiply by3 →12:15. Combine →8:12:15.
