Pak Army Civilian Posts: GD Clerk / LDC Mathematics Ratio & Proportion — Set 3

Ratio & Proportion MCQs set 3 for Pak Army Civilian Posts: GD Clerk / LDC Mathematics — 20 solved questions.

Pak Army Civilian Posts: GD Clerk / LDC Mathematics Ratio & Proportion — Set 3

  1. Question 1

    Q1. The salaries of A, B and C are in the ratio 1:3:4. If the salaries are increased by 5%, 10% and 15% respectively, then the increased salaries will be in the ratio?

    • A) 21:66:92
    • B) 0.7878125
    • C) 32:67:93
    • D) None of these

    Answer: 21:66:92

    Explanation: The correct value is 21:66:92. Apply the formula or arithmetic step shown in the question and

  2. Question 2

    Q2. Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

    • A) 4:03:02
    • B) 2:03:04
    • C) 3:04:02
    • D) None of these

    Answer: 2:03:04

    Explanation: The correct value is 2:03:04. Apply the formula or arithmetic step shown in the question and

  3. Question 3

    Q3. The third proportional to 3.5, 5.6 is:___________?

    • A) 8.96
    • B) 8
    • C) 4.5
    • D) 6.2

    Answer: 8.96

    Explanation: Third proportional to a and b is b²/a = 5.6² ÷ 3.5 = 31.36 ÷ 3.5 = 8.96.

  4. Question 4

    Q4. A cylinder and a cone have a same height and same radius of the base. The ratio between the volumes of the cylinder and cone is__________?

    • A) 5:01
    • B) 3:01
    • C) 2:01
    • D) 1:05

    Answer: 3:01

    Explanation: Both share the same base and height; volume of cylinder = πr²h and cone = (1/3)πr²h, so their ratio is 3:1.

  5. Question 5

    Q5. A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both he must invest the money in the ratio_________?

    • A) 16:15
    • B) 15:16
    • C) 12:11
    • D) 11:12

    Answer: 16:15

    Explanation: Income per rupee invested: 9% stock at 96 yields 9/96; 12% stock at 120 yields 12/120 = 1/10. For equal dividends, invest in ratio (9/96):(1/10) inverted = 96/9 : 10 = 32:30/3 → 16:15.

  6. Question 6

    Q6. Two cylinders are of the same height. Their radii are in the ratio 1: 3. If the volume of the first cylinder is 40 cc. Find the volume of the second cylinder?

    • A) 360 cc
    • B) 60 cc
    • C) 300 cc
    • D) 36 cc

    Answer: 360 cc

    Explanation: Volume of a cylinder is proportional to r². With radii in ratio 1:3, volumes are in ratio 1:9. Second cylinder's volume = 40 × 9 = 360 cc.

  7. Question 7

    Q7. The mean of 5 numbers is 34. Three of these numbers are 29, 26, and 35. If the remaining two numbers are in the ratio 1:3, what are the numbers?

    • A) 10, 40
    • B) 20, 60
    • C) 35, 45
    • D) None of these

    Answer: 20, 60

    Explanation: The correct value is 20, 60. Apply the formula or arithmetic step shown in the question and

  8. Question 8

    Q8. The number of seats available for Biology and Computer Science in a school is in the ratio 5:8. They are to be increased by 30% and 25% . Find the new ratio.

    • A) 20:13
    • B) 13:20
    • C) 11:20
    • D) 20:11

    Answer: 13:20

    Explanation: New seats: Biology = 5×1.3 = 6.5, Computer Science = 8×1.25 = 10; ratio = 6.5:10 = 13:20.

  9. Question 9

    Q9. Which of the following is a rational number?

    • A) √3
    • B) π
    • C) √5
    • D) 04-May

    Answer: 04-May

    Explanation: A rational number can be expressed as p/q where p and q are integers. 4/5 satisfies this, while √3, π, and √5 are irrational.

  10. Question 10

    Q10. The ratio of the length to the breadth of a rectangle is 3:2. Its area is 2400 m². What is the length of the field?

    • A) 20 m
    • B) 40 m
    • C) 60 m
    • D) 70 m

    Answer: 60 m

    Explanation: Let length = 3k and breadth = 2k; area = 6k² = 2400, so k² = 400, k = 20; length = 3 × 20 = 60 m.

  11. Question 11

    Q11. If 80% of the applications to a program were rejected, what is the ratio of the number of applications accepted to the number rejected?

    • A) 1:02
    • B) 1:04
    • C) 1:08
    • D) 1:16

    Answer: 1:04

    Explanation: 20% accepted and 80% rejected gives an accepted-to-rejected ratio of 20:80 = 1:4.

  12. Question 12

    Q12. The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy?

    • A) 15
    • B) 9
    • C) 18
    • D) 21

    Answer: 9

    Explanation: Total age of three boys = 3 × 15 = 45; ratio 3:5:7 sums to 15 parts; youngest's age = (3/15) × 45 = 9 years.

  13. Question 13

    Q13. Find the value of x when y = 5, if x varies directly as 4y-1 and x = 14 when y = 2. Proportion

    • A) 38
    • B) 35
    • C) 10
    • D) 28

    Answer: 38

    Explanation: x ∝ (4y − 1): when y = 2, 4y−1 = 7 and x = 14, giving constant k = 2; when y = 5, x = 2 × (4×5−1) = 38.

  14. Question 14

    Q14. Milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively in what ratio the liquids in both the vessels should be mixed to obtain a new mixture in vessel C containing half milk and half water?

    • A) 1:01
    • B) 1:03
    • C) 5:02
    • D) 7:05

    Answer: 7:05

    Explanation: Milk fractions: A = 4/7, B = 2/5, target = 1/2. By alligation: (1/2−2/5):(4/7−1/2) = (1/10):(1/14) = 7:5.

  15. Question 15

    Q15. Kashif and Nadeem jointly started a business. Kashif invested three times as Nadeem did and invested his money for double time as compared to Nadeem. Nadeem earned Rs. 4000. If the gain is proportional to the money invested and the time for which the

    • A) Rs0.16
    • B) Rs0.20
    • C) Rs0.24
    • D) Rs0.28

    Answer: Rs0.28

    Explanation: Kashif's investment ratio = 3 × 2 = 6 times Nadeem's. If Nadeem earned Rs. 4000, Kashif earned 6 × 4000 = Rs. 24,000.

  16. Question 16

    Q16. In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?

    • A) 50
    • B) 100
    • C) 150
    • D) 200

    Answer: 150

    Explanation: Let coin counts be x, 2x, 3x; total value 25x + 20x + 15x = 60x paise = Rs. 30, so x = 50 and the 5p coins number 3×50 = 150.

  17. Question 17

    Q17. In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180-gram mixture, 36 grams of pure milk is added, what would be the percentage of milk in the mixture formed?

    • A) 80.20%
    • B) 100%
    • C) 83.33%
    • D) None of these

    Answer: 83.33%

    Explanation: The correct value is 83.33%. Apply the formula or arithmetic step shown in the question and

  18. Question 18

    Q18. Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R

    • A) 05-Nov
    • B) 06-Nov
    • C) 07-Nov
    • D) 08-Nov

    Answer: 06-Nov

    Explanation: Combined fill rate = 1/30+1/20+1/10 = 11/60. Pipe C's contribution = (1/10)/(11/60) = 6/11 of the total solution.

  19. Question 19

    Q19. The ratio of ducks and frogs is a pond is 37:39 respectively. The average number of ducks and frogs in the pond is 152. What is the number of frogs in the pond?

    • A) 148
    • B) 152
    • C) 156
    • D) 144

    Answer: 156

    Explanation: Total ducks + frogs = 2 × 152 = 304. Frogs = (39/76) × 304 = 156.

  20. Question 20

    Q20. p is 50% more than q. Find the ratio of p to q.

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

    Answer: 3:02

    Explanation: If p = 1.5q, then p:q = 3:2. Show the calculation clearly when solving similar quantitative items.

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Level 1

The salaries of A, B and C are in the ratio 1:3:4. If the salaries are increased by 5%, 10% and 15% respectively, then the increased salaries will be in the ratio?