Free Ratio and Proportion MCQs with Answers
293 Ratio and Proportion MCQs from Mathematics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
Ratios compare quantities in the same units, while proportions state that two ratios are equal. Problems cover simplification, division in a given ratio, direct and inverse variation, scale, and missing terms, with attention to the difference between a ratio and a fraction representing part of a whole.
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293 questions · page 11 of 15
- A. 51
- B. 61
- C. 47
- D. 45
Explanation: To minimise the number of equal casks, use the greatest common capacity: HCF(435 L, 493 L, 551 L) = 29 L.
Correct answer: 51- A. 53
- B. 112
- C. 108
- D. 106
Explanation: If the remainders are equal, the greatest divisor must divide the differences between the numbers.
Correct answer: 106- A. 12
- B. 18
- C. 24
- D. 32Everyday Science Quiz
Explanation: A divisor giving the same remainder to all three numbers must divide their pairwise differences.
Correct answer: 24- A. 700,400
- B. 820,360
- C. 800,500
- D. 820,369
Explanation: Work backwards through the Euclidean algorithm with final divisor 41. The pair 820 and 369 gives 820 = 2 x 369 + 82, 369 = 4 x 82 + 41…
Correct answer: 820,369- A. 3600
- B. 504
- C. 441
- D. 7056
Explanation: The LCM of 21, 36 and 56 is 2^3 x 3^2 x 7 = 504. To make this a perfect square, the odd power of 2 must be supplied by another factor of…
Correct answer: 7056- A. 36
- B. 66
- C. 132
- D. 264
Explanation: For two numbers, product = HCF x LCM. Thus the product is 12 x 396 = 4752, and the other number is 4752 ÷ 36 = 132.
Correct answer: 132- A. 1080
- B. 10080
- C. 10025
- D. 11080
Explanation: The LCM of 12, 15 and 18 is 180. The first five-digit multiple is 180 x 56 = 10080, because 180 x 55 = 9900 is still four digits.
Correct answer: 10080- A. 31
- B. 41
- C. 51
- D. 61
Explanation: The number must leave remainder 1 when divided by 2, 3 and 5, so it is 1 more than a multiple of LCM(2, 3, 5) = 30.
Correct answer: 31- A. 1439
- B. 1440
- C. 1459
- D. 1449Pakistan Studies Quiz
Explanation: If the number increased by 1 is divisible by all the given numbers, first find their LCM: LCM(12, 18, 24, 32, 40) = 1440.
Correct answer: 1439- A. 10085
- B. 10080
- C. 10075
- D. 10070
Explanation: The least five-digit multiple of 144 is found by taking the first multiple at or above 10000: 144 x 69 = 9936, while 144 x 70 = 10080.
Correct answer: 10080- A. 9930
- B. 9903
- C. 9935
- D. 9936
Explanation: The greatest four-digit multiple of 144 is obtained from 144 x 69 = 9936; the next multiple, 144 x 70 = 10080, has five digits.
Correct answer: 9936- A. 1080
- B. 1085
- C. 1075
- D. 1095
Explanation: The least common multiple of 4, 6, 8 and 10 is 120, since 120 is the smallest number divisible by all four.
Correct answer: 1080- A. 90730
- B. 90725
- C. 90715
- D. 90720
Explanation: The LCM of 32, 36, 40, 42 and 48 is 2^5 x 3^2 x 5 x 7 = 10080. The greatest five-digit multiple is 10080 x 9 = 90720, because 10080 x 10 =…
Correct answer: 90720- A. (36,60)
- B. (12,180)
- C. (96,25)
- D. (72,30)
Explanation: For 36 and 60, the product is 36 x 60 = 2160 and their HCF is 12, since both divide by 12 but have no larger common divisor.
Correct answer: (36,60)- A. 246 seconds
- B. 242 seconds
- C. 240 seconds
- D. 243 seconds
Explanation: The bells toll together after the LCM of their intervals: LCM(8, 10, 12, 16) = 2^4 x 3 x 5 = 240 seconds.
Correct answer: 240 seconds- A. 71
- B. 70
- C. 69
- D. 68
Explanation: The LCM of 8, 12 and 18 is 2^3 x 3^2 = 72. Therefore the least intended number is 72 - 3 = 69, because adding 3 gives 72, which is…
Correct answer: 69- A. 982
- B. 893
- C. 1024
- D. 995
Explanation: Test the congruences for 995: 995 = 16 x 62 + 3, 995 = 18 x 55 + 5, and 995 = 21 x 47 + 8.
Correct answer: 995- A. 2040
- B. 2010
- C. 135
- D. 150
Explanation: For two positive integers, product = HCF x LCM. Therefore LCM = 2025 / 15 = 135.
Correct answer: 135- A. 34
- B. 17
- C. 85
- D. 204
Explanation: Using the Euclidean algorithm, gcd(204, 1190) = gcd(204, 170) = 34, and gcd(34, 1445) = 17. Therefore the HCF of all three numbers is 17.
Correct answer: 17- A. 1
- B. 2
- C. 3
- D. 4
Explanation: The common factors are found successively: gcd(12, 16) = 4, gcd(4, 18) = 2, and gcd(2, 24) = 2. Thus the HCF is 2.
Correct answer: 2