Numerical: Ratio & Proportion MCQ — 15 Practice Questions with Answers

Explanation

In a ratio division question, first add the ratio parts. Here the ratio is 3 : 5, so total parts = 3 + 5 = 8. Ramesh gets 3 parts out of these 8 parts. Therefore, Ramesh's share = Total amount × Ramesh's parts ÷ Total parts = 640 × 3 ÷ 8. Since 640 ÷ 8 = 80, his share is 80 × 3 = ₹240. Hence, Ramesh's share is ₹240.

Explanation

Let the two original numbers be 7x and 9x. After adding 16 to each, the ratio is (7x + 16) : (9x + 16) = 9 : 11. Therefore, 11(7x + 16) = 9(9x + 16). This gives 77x + 176 = 81x + 144, so 32 = 4x and x = 8. The numbers are 56 and 72. Hence the statement saying that the larger number is 80 is incorrect.

Explanation

For item 1, total ratio parts = 2 + 5 = 7. One part = ₹210 ÷ 7 = ₹30, so the larger share = 5 × ₹30 = ₹150. For item 2, mean proportional between a and b is √(a × b). Thus √(16 × 81) = √1296 = 36. For item 3, cost of 1 pen = ₹45 ÷ 3 = ₹15, so cost of 8 pens = 8 × ₹15 = ₹120. The correct matching is 1-150, 2-36, 3-120.

Explanation

In a proportion a:b = c:d, the product of extremes equals the product of means. Here, 12:18 = x:45, so 12 × 45 = 18 × x. Thus 540 = 18x, and x = 540 ÷ 18 = 30. The same result also comes from reducing 12:18 to 2:3; if 3 parts become 45, then 2 parts become 30. Hence x = 30.

Explanation

To combine two ratios, make the common term B equal in both ratios. In A:B = 2:3 and B:C = 4:5, the B values are 3 and 4. Their LCM is 12. Multiply 2:3 by 4 to get A:B = 8:12. Multiply 4:5 by 3 to get B:C = 12:15. Now B is common, so A:B:C = 8:12:15. Therefore, A:C = 8:15.