Ratio, Ages, Mixtures and Mensuration MCQs

Ratio and proportion, problems on ages, mixtures and partnership, and area, perimeter and volume of common shapes, with worked solutions.

1. 1

   Two numbers are in the ratio 5 : 7 and their difference is 24. What is the larger number?

   A60B84C72D96

   Correct answer: B. 84

   The difference is 2 parts = 24, so one part = 12. Larger number = 7 × 12 = 84.

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2. 2

   If A : B = 2 : 3 and B : C = 4 : 5, what is A : B : C?

   A8 : 12 : 5B8 : 12 : 15C2 : 3 : 5D6 : 12 : 15

   Correct answer: B. 8 : 12 : 15

   Make B the same in both ratios: multiply the first by 4 and the second by 3. A : B = 8 : 12 and B : C = 12 : 15, so A : B : C = 8 : 12 : 15.

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3. 3

   ₹1,800 is divided among A, B and C in the ratio 2 : 3 : 4. What is C's share?

   A₹900B₹800C₹600D₹400

   Correct answer: B. ₹800

   Total parts = 9; one part = ₹200. C gets 4 parts = ₹800.

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4. 4

   Find the fourth proportional to 4, 9 and 12.

   A18B36C27D24

   Correct answer: C. 27

   4 : 9 = 12 : x, so x = 9 × 12 ÷ 4 = 27.

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5. 5

   What is the mean proportional between 4 and 16?

   A12B6C10D8

   Correct answer: D. 8

   Mean proportional = √(4 × 16) = √64 = 8.

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6. 6

   A father is three times as old as his son. After 15 years he will be twice as old as his son. What is the father's present age?

   A50 yearsB40 yearsC45 yearsD48 years

   Correct answer: C. 45 years

   Let the son be x. Then 3x + 15 = 2(x + 15), so x = 15 and the father is 3 × 15 = 45 years old.

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7. 7

   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?

   A24 yearsB19 yearsC21 yearsD29 years

   Correct answer: C. 21 years

   Five years ago the sum was 50 − 10 = 40, split 3 : 2 as 24 and 16. So now A = 29 and B = 16 + 5 = 21 years.

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8. 8

   The present ages of two sisters are in the ratio 4 : 5. After 6 years the ratio will be 5 : 6. What is the elder sister's present age?

   A25 yearsB24 yearsC36 yearsD30 years

   Correct answer: D. 30 years

   Let the ages be 4k and 5k. (4k + 6) : (5k + 6) = 5 : 6 gives 24k + 36 = 25k + 30, so k = 6. The elder sister is 5 × 6 = 30 years old.

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9. 9

   The average age of 5 children is 8 years. When their teacher's age is included, the average becomes 12 years. How old is the teacher?

   A32 yearsB34 yearsC40 yearsD30 years

   Correct answer: A. 32 years

   Total with teacher = 12 × 6 = 72; children's total = 40. Teacher = 32 years.

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10. 10

    A 40-litre mixture has milk and water in the ratio 3 : 1. How much water must be added to make the ratio 1 : 1?

    A10 litresB20 litresC30 litresD15 litres

    Correct answer: B. 20 litres

    Milk = 30 L and water = 10 L. For a 1 : 1 ratio water must also be 30 L, so add 30 − 10 = 20 L.

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12. 11

    In what ratio must rice at ₹40/kg be mixed with rice at ₹60/kg to get a mixture worth ₹46/kg?

    A3 : 7B2 : 3C1 : 1D7 : 3

    Correct answer: D. 7 : 3

    By alligation: cheaper : dearer = (60 − 46) : (46 − 40) = 14 : 6 = 7 : 3.

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13. 12

    A invests ₹6,000 for 12 months and B invests ₹8,000 for 6 months in a business. Out of a profit of ₹7,000, what is A's share?

    A₹3,000B₹4,000C₹2,800D₹4,200

    Correct answer: D. ₹4,200

    Profit is shared by capital × time: A = 72,000 and B = 48,000, a ratio of 3 : 2. A gets 3/5 × 7,000 = ₹4,200.

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14. 13

    What is the area of a rectangle 15 m long and 8 m wide?

    A120 m²B46 m²C23 m²D240 m²

    Correct answer: A. 120 m²

    Area = length × width = 15 × 8 = 120 m². (46 m would be the perimeter.)

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15. 14

    The area of a square is 196 m². What is its perimeter?

    A56 mB28 mC98 mD49 m

    Correct answer: A. 56 m

    Side = √196 = 14 m, so perimeter = 4 × 14 = 56 m.

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16. 15

    Find the area of a circle of radius 14 cm (take π = 22/7).

    A616 cm²B88 cm²C1,232 cm²D308 cm²

    Correct answer: A. 616 cm²

    Area = πr² = 22/7 × 14 × 14 = 616 cm². (88 cm is the circumference.)

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17. 16

    Find the circumference of a circle of radius 21 cm (take π = 22/7).

    A132 cmB264 cmC66 cmD1,386 cm

    Correct answer: A. 132 cm

    Circumference = 2πr = 2 × 22/7 × 21 = 132 cm.

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18. 17

    What is the volume of a cube with sides of 6 cm?

    A36 cm³B108 cm³C216 cm³D72 cm³

    Correct answer: C. 216 cm³

    Volume = side³ = 6 × 6 × 6 = 216 cm³.

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19. 18

    Find the volume of a cylinder with radius 7 cm and height 10 cm (take π = 22/7).

    A154 cm³B1,540 cm³C440 cm³D3,080 cm³

    Correct answer: B. 1,540 cm³

    Volume = πr²h = 22/7 × 7 × 7 × 10 = 1,540 cm³.

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20. 19

    What is the area of a triangle with base 12 cm and height 9 cm?

    A42 cm²B21 cm²C54 cm²D108 cm²

    Correct answer: C. 54 cm²

    Area = ½ × base × height = ½ × 12 × 9 = 54 cm².

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21. 20

    If each side of a square is increased by 20%, by what percent does its area increase?

    A40%B20%C24%D44%

    Correct answer: D. 44%

    New area = 1.2 × 1.2 = 1.44 times the old, an increase of 44%.

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