MCQ
Numerical: ratio & proportion MCQ - Practice Questions with Answers
Solve 14 Numerical: ratio & proportion questions for RAS/RPSC preparation.
Practice questions
Q1Amit, Sumit and Vinay divide an amount of ₹ 2800 among themselves in the ratio 5 : 6 : 3, respectively. If ₹ 200 is added to each person's share, what will be the new ratio of their shares?
The total ratio parts are 5 + 6 + 3 = 14. Since ₹ 2800 is divided into 14 parts, one part is ₹ 200. Amit gets ₹ 1000, Sumit gets ₹ 1200 and Vinay gets ₹ 600. After adding ₹ 200 to each share, the amounts become ₹ 1200, ₹ 1400 and ₹ 800. Dividing by 200 gives 6 : 7 : 4. The ratios 6 : 9 : 4, 7 : 8 : 5 and 4 : 5 : 2 do not match these three revised amounts.
Q2The price of a gold biscuit is directly proportional to the square of its weight. A person broke the gold biscuit in the ratio 3 : 2 : 1 by weight and faced a loss of ₹ 4,840. Find the initial price of the gold biscuit.
Let the three parts have weights 3x, 2x and x. Since price is proportional to the square of weight, the original price is proportional to (6x)^2 = 36x². After breaking, the combined price is proportional to 9x² + 4x² + x² = 14x². The loss is therefore 22 parts, equal to ₹ 4,840, so one part is ₹ 220. The original price is 36 × 220 = ₹ 7,920. ₹ 7,000, ₹ 7,200 and ₹ 8,000 do not satisfy this 36:14 price comparison.
Q3If the ratio of the areas of two equilateral triangles is 36 : 25, then the ratio of their perimeters will be:
For similar figures, the ratio of areas is the square of the ratio of corresponding sides. Equilateral triangles are always similar, so if their areas are in the ratio 36 : 25, their side ratio is the square root, 6 : 5. The perimeter of an equilateral triangle is three times its side, so the perimeter ratio is also 6 : 5. Ratios such as 12 : 5, 25 : 16, and 36 : 25 confuse area ratio with side or perimeter ratio.
Q4If the lengths of the diagonals of two squares are in the ratio 4 : 7, then what is the ratio of their areas?
In a square, the diagonal is side times root 2, so the side is directly proportional to the diagonal. Area is the square of the side, so the ratio of areas is the square of the diagonal ratio. Squaring 4 : 7 gives 16 : 49. The ratio 4 : 7 only compares the diagonals, not the areas. The ratio 64 : 343 cubes the terms and therefore fits volume-style reasoning, not area. The ratio 2 : 1 has no relation to the given diagonal ratio.
Q5If A’s income is 3/5 times B’s income and C’s income is 6/5 times B’s income, then the ratio of C’s income to A’s income is:
Let B’s income be x. Then A’s income is 3x/5 and C’s income is 6x/5. The required ratio is C : A = 6x/5 : 3x/5. Since both terms have x/5 in common, it cancels out, leaving 6 : 3, which reduces to 2 : 1. The ratio 1 : 2 reverses the order, 1 : 1 would mean equal incomes, and 3 : 1 does not follow from the given fractions.
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More questions
6The ratio between the present ages of Sudhir and Sanjay is 4 : 5. After 5 years, the ratio between their ages will become 5 : 6. The present age of Sudhir is:
7An iron rod of uniform thickness and length 5.6 metres weighs 2.4 kg. What will be the weight of 5 iron rods of the same thickness, each having a length of 8.4 metres?
8If m is proportional to n and m = 5 when n = 4, then what is the value of m when n = 20?
9If the income of x is 10% more than that of y and the income of y is 20% less than that of z, then the incomes of x, y and z respectively are in the ratio:
10An amount of ₹ 3550 is divided among X, Y and Z such that three times X's share is equal to 5 times Y's share and 7 times Z's share. What is X's share?
11A bag contains only 50-paisa, 25-paisa and 10-paisa coins. The ratio of the number of 50-paisa, 25-paisa and 10-paisa coins is 5 : 8 : 3. If the total value of all the coins in the bag is ₹ 144, then how many 25-paisa coins are there in the bag?
12A sum of money is to be distributed among P, Q, R and S in the ratio 6 : 2 : 5 : 3. If R gets ₹ 2,000 more than S, what is Q's share?
13Two numbers are in the ratio 21 : 26. If 8 is added to each number, the new numbers are in the ratio 5 : 6. Find the ratio of the numbers if 2 is subtracted from each number.
14The incomes of Mr. Dhull and Mr. Hussain are in the ratio 7 : 4, and their expenditures are in the ratio 2 : 1. If each saves ₹ 10,000, then Mr. Dhull's expenditure is: