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The MCQs below are drawn from the Mathematics subject category.
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7241
If 5A = 7B = 9C, then A : B : C is:
A. 63 : 45 : 35
B. 35 : 45 : 63
C. 45 : 63 : 35
D. 63 : 35 : 45
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Correct Option
Explanation
A = k/5, B = k/7, C = k/9. Ratio = 1/5 : 1/7 : 1/9. Multiply by LCM(5,7,9) = 315. 315/5 : 315/7 : 315/9 = 63 : 45 : 35.
7242
What number must be subtracted from each term of the ratio 17:33 so that it becomes 7:15?
A. 2
B. 3
C. 4
D. 5
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Correct Option
Explanation
Let x be subtracted. (17 - x) / (33 - x) = 7 / 15. Cross-multiply: 15(17 - x) = 7(33 - x) => 255 - 15x = 231 - 7x => 8x = 24 => x = 3.
7243
Divide 50 into two parts so that the sum of their reciprocals is 1/12. What are the two parts?
A. 20, 30
B. 24, 26
C. 28, 22
D. 35, 15
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Explanation
Let parts be x and 50-x. 1/x + 1/(50-x) = 1/12. (50-x+x) / (x(50-x)) = 1/12 => 50 / (50x - x^2) = 1/12 => 600 = 50x - x^2. Solving x^2 - 50x + 600 = 0 gives (x-20)(x-30) = 0. Parts are 20 and 30.
7244
The ratio of the angles of a triangle is 2:3:4. What is the measure of the smallest angle?
A. 20 degrees
B. 40 degrees
C. 60 degrees
D. 80 degrees
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Explanation
Sum of angles of a triangle is 180. Total parts = 2+3+4 = 9. 1 part = 180/9 = 20. Smallest angle = 2 parts = 2 * 20 = 40 degrees.
7245
The ratio of copper and zinc in brass is 13:7. How much zinc will be there in 100 kg of brass?
A. 20 kg
B. 35 kg
C. 55 kg
D. 65 kg
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Explanation
Total parts = 13 + 7 = 20. Zinc share = (7/20) * 100 = 35 kg.
7246
If x : y = 3 : 2, then the ratio 2x^2 + 3y^2 : 3x^2 - 2y^2 is equal to:
A. 12 : 5
B. 6 : 5
C. 30 : 19
D. 5 : 3
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Correct Option
Explanation
Substitute x=3, y=2: Numerator = 2(9) + 3(4) = 18 + 12 = 30. Denominator = 3(9) - 2(4) = 27 - 8 = 19. Ratio is 30 : 19.
7247
Two numbers are in the ratio 1:3. If their sum is 240, then their difference is:
A. 120
B. 108
C. 96
D. 84
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Correct Option
Explanation
Let numbers be x and 3x. Sum = 4x = 240 => x = 60. Difference = 3x - x = 2x = 2 * 60 = 120.
7248
The ratio of the number of boys to girls in a school of 720 students is 7:5. How many more girls should be admitted to make the ratio 1:1?
A. 90
B. 120
C. 150
D. 240
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Correct Option
Explanation
Total parts = 12. 1 part = 720/12 = 60. Boys = 7*60=420. Girls = 5*60=300. To make ratio 1:1, girls must be equal to boys (420). Girls to be added = 420 - 300 = 120.
7249
If an amount of Rs. 990 is divided among A, B, and C in the ratio 3:4:2, then B will get:
A. Rs. 220
B. Rs. 330
C. Rs. 440
D. Rs. 550
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Explanation
Total parts = 3+4+2 = 9. B's share = (4/9) * 990 = 4 * 110 = Rs. 440.
7250
If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?
A. 2:5
B. 3:7
C. 5:3
D. 7:3
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Correct Option
Explanation
0.4A = (2/3)B => (2/5)A = (2/3)B => A/B = (2/3) * (5/2) = 5/3. Ratio is 5:3.
