Ratio and Proportion – mcqpedia.in

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[Concept: Basic Division of Amount] If an amount of Rs 1500 is to be divided between A and B in the ratio 3:2, what will be A’s share?

Rs 900
Rs 600
Rs 1000
Rs 500

Explanation: Book Formula: Part of A = [m / (m+n)] × R. Here, m=3, n=2, R=1500. Part of A = [3 / (3+2)] × 1500 = (3/5) × 1500 = 3 × 300 = Rs 900.

[Concept: Basic Division of Amount] An amount is divided between X and Y in the ratio 5:4. If the total amount is Rs 4500, what is the difference between their shares?

Rs 500
Rs 400
Rs 900
Rs 1000

Explanation: Book Formula: Difference = [(m – n) / (m + n)] × R. Here, m=5, n=4, R=4500. Difference = [(5 – 4) / (5 + 4)] × 4500 = (1/9) × 4500 = Rs 500.

[Concept: Division Based on Difference] The ratio of shares of A and B is 7:4. If A gets Rs 1200 more than B, find the total amount distributed.

Rs 4400
Rs 2800
Rs 1600
Rs 3600

Explanation: Book Formula: Sum of parts = [(m + n) / (m – n)] × Difference. Here, m=7, n=4, Difference = 1200. Total Amount = [(7 + 4) / (7 – 4)] × 1200 = (11 / 3) × 1200 = 11 × 400 = Rs 4400.

[Concept: Division Based on Difference] The ratio of marks of two students is 5:3. If the difference in their marks is 40, what is the score of the first student?

Explanation: Book Formula: Part of A = [m / (m – n)] × Difference. Here, m=5, n=3, Diff=40. Score of first student = [5 / (5 – 3)] × 40 = (5 / 2) × 40 = 5 × 20 = 100.

[Concept: Alligation/Mixing Ratios] Two equal glasses have milk and water in the ratio 2:1 and 3:2. If both are mixed in a third glass, what is the new ratio of milk and water?

19:11
5:3
7:5
17:13

Explanation: Book Formula: Ratio = [m/(m+n) + p/(p+q)] : [n/(m+n) + q/(p+q)]. Milk = 2/3 + 3/5 = (10+9)/15 = 19/15. Water = 1/3 + 2/5 = (5+6)/15 = 11/15. So, the new ratio is 19:11.

[Concept: Alligation/Mixing Ratios] Vessel A has alcohol and water in the ratio 1:3. Vessel B has them in 1:1. If equal quantities are mixed, find the ratio of alcohol to water in the new mixture.

Explanation: Using the formula: Alcohol = 1/4 + 1/2 = 1/4 + 2/4 = 3/4. Water = 3/4 + 1/2 = 3/4 + 2/4 = 5/4. The ratio is 3:5.

[Concept: Types of Ratios] What is the subduplicate ratio of 64:81?

8:9
4096:6561
4:9
16:27

Explanation: Book Definition: The subduplicate ratio of a:b is √a : √b. Therefore, √64 : √81 = 8:9.

[Concept: Types of Ratios] What is the triplicate ratio of 2:5?

8:125
4:25
6:15
16:625

Explanation: Book Definition: The triplicate ratio of a:b is a³ : b³. Therefore, 2³ : 5³ = 8:125.

[Concept: Mean/Third/Fourth Proportions] Find the mean proportion between 9 and 16.

Explanation: Book Formula: Mean proportion of a and b = √(ab). Mean = √(9 × 16) = √144 = 12.

[Concept: Mean/Third/Fourth Proportions] Find the fourth proportional to the numbers 4, 9, and 12.

Explanation: Book Formula: Fourth proportional of a, b, c = (bc) / a. Here, a=4, b=9, c=12. Fourth proportional = (9 × 12) / 4 = 108 / 4 = 27.

[Concept: Add/Subtract for Proportion] What number must be added to 6, 14, 18, and 38 so that they become proportional?

Explanation: Book Formula for adding ‘x’: x = (bc – ad) / [(a+d) – (b+c)]. Here a=6, b=14, c=18, d=38. x = (14×18 – 6×38) / [(6+38) – (14+18)] = (252 – 228) / (44 – 32) = 24 / 12 = 2.

[Concept: Add/Subtract for Proportion] What number must be subtracted from 14, 17, 34, and 42 to make them proportional?

Explanation: Book Formula for subtracting ‘x’: x = (ad – bc) / [(a+d) – (b+c)]. Here a=14, b=17, c=34, d=42. x = (14×42 – 17×34) / [(14+42) – (17+34)] = (588 – 578) / (56 – 51) = 10 / 5 = 2.

[Concept: Componendo & Dividendo] If x/y = 5/3, find the value of (x+y)/(x-y).

Explanation: By Componendo and Dividendo rule: If a/b = c/d, then (a+b)/(a-b) = (c+d)/(c-d). So, (x+y)/(x-y) = (5+3)/(5-3) = 8/2 = 4.

[Concept: Componendo & Dividendo] If (a+b)/(a-b) = 7/2, what is the ratio of a:b?

9:5
5:9
7:2
14:4

Explanation: Applying Componendo and Dividendo again on (a+b)/(a-b) = 7/2 gives a/b = (7+2)/(7-2) = 9/5. So the ratio is 9:5.

[Concept: Finding Combined Ratios] If 2A = 3B = 4C, find the ratio A:B:C.

6:4:3
2:3:4
4:3:2
12:8:6

Explanation: Book Method: Take the LCM of the coefficients (2, 3, 4), which is 12. Then divide the LCM by each coefficient: A = 12/2 = 6, B = 12/3 = 4, C = 12/4 = 3. Therefore, A:B:C = 6:4:3.

[Concept: Finding Combined Ratios] If A:B = 2:3 and B:C = 4:5, find the ratio A:B:C.

8:12:15
2:12:5
6:12:15
8:15:12

Explanation: Book Method: Make B common. Multiply the first ratio by 4 (coeff of B in 2nd) and the second ratio by 3 (coeff of B in 1st). A:B = 8:12, B:C = 12:15. Combined A:B:C = 8:12:15.

[Concept: Concept of Degree] If a/b = 4/3, what is the value of (3a+2b)/(3a-2b)?

3
2
4
Cannot be determined

Explanation: Book Note: To solve this type of equation, the degree of each term must be the same (homogeneous). Here, all terms have degree 1. We can directly substitute a=4, b=3. (3*4 + 2*3) / (3*4 – 2*3) = (12+6) / (12-6) = 18/6 = 3.

[Concept: Concept of Degree] If x/y = 2/5, what is the value of (x² + y) / (x + y²)?

Cannot be determined
9/27
2/5
4/25

Explanation: Book Note: The expression cannot be determined because the degree of each term is not the same. The numerator has degree 2 and 1, and the denominator has degree 1 and 2.