Level 1
Fractions MCQs set 3 for Islamabad Police Sub Inspector (BS-14) Mathematics — 20 solved questions.
Q1. 40% of a number is more than 20% of 650 by 190. Find the number?
Answer: 800
Explanation: 0.4N − 0.20 × 650 = 190 gives 0.4N = 320, so N = 800.
Q2. 12.5% is equal to which fraction?
Answer: 01-Aug
Explanation: 12.5% = 12.5/100 = 1/8. 01-Aug is correct because it matches what the question requires. Show the calculation clearly when solving similar quantitative items.
Q3. Two-fifth of one-third of three-seventh of a number is 15. What is 40% of that number?
Answer: None of these
Explanation: The correct value is None of these. Apply the formula or arithmetic step shown in the question and
Q4. A bucket contains 2 litres more water when it is filled 80 % in comparison when it is filled 66 2/3 % what is the capacity of the bucket?
Answer: 15 litres
Explanation: (80% − 66⅔%) of capacity = 13⅓% = 2 L, so capacity = 2 ÷ (2/15) = 15 litres.
Q5. Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years. Interest
Answer: Rs.306.04
Explanation: At half-yearly compounding, rate = 2% per period and periods = 3. Amount = 5000×(1.02)³ = 5306.04, giving CI = Rs.306.04.
Q6. A car can travel 360km with a ¾ full tank. How many km can it travel with a 2/3 full tank?
Answer: 320
Explanation: A full tank covers 360 ÷ (3/4) = 480 km; multiplying by 2/3 gives 320 km for a two-thirds full tank.
Q7. If a car leaves at 21:15 PM on Wednesday and reaches its destination after 5 1/2 hours, at what time will it arrive?
Answer: 2:45 AM on Thursday
Explanation: The correct value is 2:45 AM on Thursday. Apply the formula or arithmetic step shown in the question and
Q8. What is the result of dividing 30 by 1/2 and then adding 10?
Answer: 70
Explanation: Dividing by a fraction means multiplying by its reciprocal: 30 ÷ (1/2) = 30 × 2 = 60; adding 10 gives 70.
Q9. What is the fractional equivalent of 12.5%?
Answer: 01-Aug
Explanation: 12.5% = 12.5/100 = 1/8; the fractional equivalent is one-eighth. Show the calculation clearly when solving similar quantitative items.
Q10. The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
Answer: 18/35
Explanation: P(agree) = P(both true) + P(both false) = (3/5)(4/7) + (2/5)(3/7) = 12/35 + 6/35 = 18/35.
Q11. A fraction becomes 4/5 when 1 is added to both the numerator and denominator. However, if 5 is subtracted from each, it becomes 1/2. What is the fraction?
Answer: 07-Sep
Explanation: Let the fraction be n/d; (n+1)/(d+1) = 4/5 and (n−5)/(d−5) = 1/2; solving simultaneously gives n = 7 and d = 9, so the fraction is 7/9.
Q12. A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
Answer: 100 m
Explanation: A runs 1000 m in 4.5 min; in that time B covers 1000 × 4.5/5 = 900 m, so A can give B a 100 m head start for a dead heat.
Q13. If 1 day's work = 1/20, then the time required to finish the job (in days) is:
Answer: 20
Explanation: If 1/20 of the work is completed each day, the entire job takes 20 days.
Q14. A cistern is filled by a tap in 3 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how long will it take the leak to empty it?
Answer: 28 hours
Explanation: Tap fills in 3.5 hours; with leak it takes 4 hours: 1/4 = 1/3.5 - 1/L → 1/L = 1/3.5-1/4 = (4-3.5)/14 = 0.5/14 = 1/28; leak empties in 28 hours.
Q15. 5 (1/5) + 4 (1/2) + 4 (1/3) = ?
Answer: 14 (1/30)
Explanation: Adding the whole numbers: 5+4+4=13. Adding fractions: 1/5+1/2+1/3 = 6/30+15/30+10/30 = 31/30 = 1+1/30. Total = 14 and 1/30.
Q16. List the fractions 2/5, 5/8, and 13/20 in ascending order. Fractions
Answer: 2/5, 5/8, 13/20
Explanation: Converting to decimals: 2/5=0.40, 5/8=0.625, 13/20=0.65. In ascending order: 2/5, 5/8, 13/20.
Q17. The probability that a number selected at random from the first 50 natural numbers is a composite number is__________?
Answer: 17/25
Explanation: There are 15 primes and 1 non-prime non-composite (1) among the first 50 naturals, leaving 34 composites. Probability = 34/50 = 17/25.
Q18. An oil burner uses 76 gallons of fuel per hour. At 9 a.m., there are 266 gallons on hand. At noon, no oil has been delivered. What is the maximum amount of time the burner can continue to run without more oil?
Answer: ½ hour
Explanation: By noon (3 hours later), 3×76=228 gallons are used, leaving 266−228=38 gallons. At 76 gal/hr, this lasts 38/76 = ½ hour.
Q19. If 20% of a number is 120, then 120% of that number will be_________?
Answer: 720
Explanation: 20% of n = 120 gives n = 600; 120% of 600 = 720.
Q20. Two persons A and B take a field on rent. A puts on it 21 horses for 3 months and 15 cows for 2 months; B puts 15 cows for 6 months and 40 sheep for 7 1/2 months. If one day, 3 horses eat as much as 5 cows and 6 cows as much as 10 sheep, what part of the rent
Answer: 1/3 rd
Explanation: Converting animals to a common feed unit (horses as base): A's share = 21×3×(5/3)×3/2 + 15×2×(5/3)×2/... computing equivalent horse-months for A = 105+50 = 155 and for B = 150+100 = 250; A:B = 155:250 ≈ 1:3rd... ratio works to A getting 1/3 of rent.