National Highways & Motorway Police (NH&MP) Constable Mathematics Ratio & Proportion — Set 2

Ratio & Proportion MCQs set 2 for National Highways & Motorway Police (NH&MP) Constable Mathematics — 20 solved questions.

National Highways & Motorway Police (NH&MP) Constable Mathematics Ratio & Proportion — Set 2

  1. Question 1

    Q1. A journey of 750 km was covered partly by car (x km) and partly by train (y km). If the distance travelled by train was 150 km more than the distance travelled by car, find x:y.

    • A) 1:02
    • B) 2:03
    • C) 3:04
    • D) 4:05

    Answer: 2:03

    Explanation: x+y = 750, y = x+150; solving: x = 300, y = 450; x:y = 2:3.

  2. Question 2

    Q2. If two positive numbers are in the ratio 1/8 : 1/5, then by what percent is the second number more than the first?

    • A) 40%
    • B) 33.33%
    • C) 60%
    • D) 66.67%

    Answer: 60%

    Explanation: Ratio 1/8 : 1/5 = 5:8; second exceeds first by (8−5)/5×100 = 60%.

  3. Question 3

    Q3. According to a recipe, 400 grams of flour should be mixed with 500 grams of sugar to bake cookies. If I have only 300 grams of flour, how much sugar should I mix to maintain the same proportion?

    • A) 360 grams
    • B) 380 grams
    • C) 375 grams
    • D) 400 grams

    Answer: 375 grams

    Explanation: Sugar needed = 300×(500/400) = 375 grams. 375 grams is correct because it matches what the question requires. Show the calculation clearly when solving similar quantitative items.

  4. Question 4

    Q4. The milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively. IN what ratio, the liquids be mixed in both the vessels so that the new liquid contains half milk and half water?

    • A) 7:05
    • B) 1:02
    • C) 2:01
    • D) 6:05

    Answer: 7:05

    Explanation: Using alligation: milk fractions 4/7 and 2/5, target 1/2; difference ratios (1/2−2/5):(4/7−1/2) = (1/10):(1/14) = 14:10 = 7:5.

  5. Question 5

    Q5. Sharjeel has a container which has a mixture of wine and water in it. Wine and water are in the ratio 4:1. Sharjeel spills some of the mixture by accident. He then replaces the spilled amount with water of same quantity. But now the wine to water ratio became 3:2.

    • A) 03-May
    • B) 01-Feb
    • C) 01-Apr
    • D) 02-Jul

    Answer: 01-Apr

    Explanation: If fraction x is removed and replaced with water: wine ratio = (4/5)(1−x)/(1/5(1−x)+x) = 3/2; solving gives x = 1/4 of the container.

  6. Question 6

    Q6. In what ratio must a grocer mix two varieties of tea worth Rs. 60 a kg and Rs. 65 a kg so that by selling the mixture at Rs. 68.20 a kg, he may gain 10%?

    • A) 3:02
    • B) 3:04
    • C) 3:05
    • D) 4:05

    Answer: 3:02

    Explanation: The cost price of the mixture must be 68.20/1.10 = 62. Using alligation: (65−62) : (62−60) = 3 : 2, so the two varieties are mixed in ratio 3:2.

  7. Question 7

    Q7. If the volumes of two cubes are in the ratio 8: 1, the ratio of their edges is_________?

    • A) 3:01
    • B) 1:03
    • C) 2:01
    • D) 1:02

    Answer: 2:01

    Explanation: Volume ratio = (edge ratio)³, so 8:1 = (edge ratio)³, giving edge ratio = ∛8 : ∛1 = 2:1.

  8. Question 8

    Q8. Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

    • A) 2:03
    • B) 3:04
    • C) 4:05
    • D) 5:06

    Answer: 4:05

    Explanation: Let the third number = 100; the first = 120, the second = 150, giving a ratio of 120:150 = 4:5.

  9. Question 9

    Q9. If the sides of two cubes are in the ratio 3: 1 the ratio of their total surface area is?

    • A) 1:09
    • B) 2:01
    • C) 9:01
    • D) 1:02

    Answer: 9:01

    Explanation: Total surface area of a cube is proportional to the square of its side. With sides in ratio 3:1, the surface area ratio is 9:1.

  10. Question 10

    Q10. If 2/3 of A = 75% of B = 0.6 of C, what is the ratio A:B:C?

    • A) 9:08:10
    • B) 8:09:10
    • C) 10:08:09
    • D) 9:10:08

    Answer: 9:08:10

    Explanation: Setting 2A/3 = 3B/4 = 3C/5 = k gives A = 3k/2, B = 4k/3, C = 5k/3. Simplifying the ratio A:B:C yields 9:8:10.

  11. Question 11

    Q11. The ratio in which the price at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce

    • A) mixture worth Rs. 6.30 a kg is _________? Mixtures 1:2
    • B) 3:02
    • C) 2:03
    • D) 4:05

    Answer: 2:03

    Explanation: Using alligation with mixture cost = 68.20/1.10 = 62... wait, the target price is Rs. 6.30. By alligation: (7.20−6.30) : (6.30−5.70) = 0.90 : 0.60 = 3:2, so the ratio of cheaper to dearer is 2:3.

  12. Question 12

    Q12. 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?

    • A) 1:02
    • B) 3:02
    • C) 5:03
    • D) 1:05

    Answer: 5:03

    Explanation: Setting 0.4x = (2/3)y gives x/y = (2/3)/0.4 = 5/3, so the first to second ratio is 5:3.

  13. Question 13

    Q13. The measures of the angles of a triangle are in the ratio 5:4:3. What is the measure of the smallest angle?

    • A) 45°
    • B) 60°
    • C) 75°
    • D) 105°

    Answer: 45°

    Explanation: Angles are in ratio 5:4:3, summing to 12 parts = 180°; smallest angle = 3/12 × 180° = 45°.

  14. Question 14

    Q14. 8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 65. How much wine did the cask hold originally?

    • A) 18 litres
    • B) 24 litres
    • C) 32 litres
    • D) 42 litres

    Answer: 24 litres

    Explanation: After four operations the wine fraction = (1 − 8/V)⁴ = 16/81. Solving gives (1−8/V) = 2/3, so V = 24 litres.

  15. Question 15

    Q15. If the length, breadth and the height of a cuboid are in the ratio 6: 5: 4 and if the total surface area is 33300 cm², then length breadth and height in cms, are respectively?

    • A) 90, 85, 60
    • B) 85, 75, 60
    • C) 90, 75, 70
    • D) 90, 75,60

    Answer: 90, 75,60

    Explanation: Let dimensions be 6k, 5k, 4k; total surface area = 2(6k×5k + 5k×4k + 4k×6k) = 2(30+20+24)k² = 148k² = 33300, so k² = 225, k = 15; dimensions = 90, 75, 60 cm.

  16. Question 16

    Q16. A circular wire of radius 42 cm is cut and bent in the form of a rectangle whose sides are in the ratio of 6:5 The smaller side of the rectangle is:_________?

    • A) 30 cm
    • B) 60 cm
    • C) 72 cm
    • D) 132 cm

    Answer: 60 cm

    Explanation: Circumference = 2π×42 = 264 cm equals the rectangle's perimeter; with sides in ratio 6:5, the smaller side = 5×(264/22) = 60 cm.

  17. Question 17

    Q17. What is the ratio of the circumference of a circle to its radius?

    • A) 1
    • B) 2π
    • C) π/2
    • D) √π

    Answer: 2π

    Explanation: Circumference C = 2πr, so C/r = 2π. Show the calculation clearly when solving similar quantitative items.

  18. Question 18

    Q18. Efficiency of Rashid and Danish are in the ratio 5:8. If Danish takes 51 days less than Rashid to complete the work, find the time taken by Rashid to complete the work. Time-Work

    • A) 85 days
    • B) 126 days
    • C) 118 days
    • D) 136 days

    Answer: 136 days

    Explanation: Efficiency ratio 5:8 means time ratio 8:5; let times be 8k and 5k. Difference 3k = 51 gives k = 17, so Rashid takes 8 × 17 = 136 days.

  19. Question 19

    Q19. Solve for x. 2x:25 = 6:(x/3) Proportion

    • A) 18
    • B) 15
    • C) 12
    • D) 5

    Answer: 15

    Explanation: Cross-multiplying 2x:(25) = 6:(x/3) gives 2x × (x/3) = 25 × 6, so 2x²/3 = 150, x² = 225, x = 15.

  20. Question 20

    Q20. The ratio of the ages of two students is 3:2. If one is 5 years older than the other, what is the age of the younger student?

    • A) 5 years
    • B) 15 years
    • C) 10 years
    • D) None of these

    Answer: 10 years

    Explanation: The correct value is 10 years. Apply the formula or arithmetic step shown in the question and

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Level 1

A journey of 750 km was covered partly by car (x km) and partly by train (y km). If the distance travelled by train was 150 km more than the distance travelled by car, find x:y.