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The MCQs below are drawn from the Mathematics subject category.
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7331
A sum of money is divided among A, B, C, and D in the ratio 3 : 4 : 9 : 10. If the share of C is Rs. 2580 more than the share of B, what is the total amount of money?
Let the shares be 3x, 4x, 9x, and 10x. Difference between C and B's share is 9x - 4x = 5x. Given 5x = 2580, so x = 516. The total amount is 3x + 4x + 9x + 10x = 26x. Total = 26 * 516 = Rs. 13416.
7332
The salaries of A, B, and C are in the ratio 2 : 3 : 5. If their salaries are incremented by 15%, 10%, and 20% respectively, what will be the new ratio of their salaries?
Let the salaries be 200, 300, and 500 for simplicity. New salary of A = 200 * 1.15 = 230. New salary of B = 300 * 1.10 = 330. New salary of C = 500 * 1.20 = 600. The new ratio is 230 : 330 : 600, which simplifies to 23 : 33 : 60.
7333
A bag contains coins of 1 Rupee, 50 paise, and 25 paise in the ratio 2 : 3 : 4. If the total amount in the bag is Rs. 45, find the number of 50 paise coins.
Let the number of 1 Rs, 50p, and 25p coins be 2x, 3x, and 4x respectively. Their values in Rupees are 2x * 1, 3x * 0.50, and 4x * 0.25. The total value is 2x + 1.5x + x = 4.5x. Given 4.5x = 45, so x = 10. Number of 50p coins = 3x = 30.
7334
Two numbers are in the ratio 3 : 5. If 9 is subtracted from each, the new ratio becomes 12 : 23. What is the smaller number?
Let 2A = 3B = 4C = k. Then A = k/2, B = k/3, C = k/4. The ratio A : B : C is (k/2) : (k/3) : (k/4). To clear the denominators, multiply by the LCM of 2, 3, and 4, which is 12. Ratio = 6 : 4 : 3.
The mean proportional between two numbers a and b is given by the square root of their product: sqrt(a * b). Here, mean proportional = sqrt(9 * 25) = sqrt(225) = 15.
Let the third proportional be x. Then 16 : 24 :: 24 : x. Using the product of extremes and means, 16 * x = 24 * 24. 16x = 576. Solving for x gives x = 576 / 16 = 36.
Let the fourth proportional be x. Then 4 : 9 :: 12 : x. In a proportion, the product of extremes equals the product of means. So, 4 * x = 9 * 12. 4x = 108, which gives x = 27.
7339
Divide Rs. 1400 between A and B in the ratio 3 : 4. What is B's share?
Let x = 3k and y = 4k. Substitute these values into the expression: (2(3k) + 3(4k)) / (3(3k) - 4k) = (6k + 12k) / (9k - 4k) = 18k / 5k. The k cancels out, leaving the ratio 18 : 5.
