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Previous Year Topic Wise Questions With Solutions: Ratio & Proportion | CSAT Preparation - UPSC PDF Download
Q1. In a T20 cricket match, three players X, Y and Z scored a total of 37 runs. The ratio of number of runs scored by X to the number of runs scored by Y is equal to the ratio of number of runs scored by Y to number of runs scored by Z. (2025)
Value-I = Runs scored by X
Value-II = Runs scored by Y
Value-III = Runs scored by Z
Which one of the following is correct?
(a) Value-I < Value-II < Value-III
(b) Value-III < Value-II < Value-I
(c) Value-I < Value-III < Value-II
(d) Cannot be determined due to insufficient data
View Answer 
Ans: (d)
As per the question,
X + Y + Z = 37
And, X/Y = Y/Z
Or Y2 = XZ
If Y = 12, then X = 9 or 16, Z = 16 or 9
So, X < Y < Z OR Z < Y < X
i.e. Value-I < Value-II < Value-III OR Value-III < Value-II < Value-I
Hence, option (d) is correct.
Q2. A person buys three articles P, Q and R for ₹ 3,330. If P costs 25% more than R and R costs 20% more than Q, then what is the cost of P? (2024)
(a) ₹ 1,000
(b) ₹ 1,200
(c) ₹ 1,250
(d) ₹ 1,350
View Answer Ans: (d)
Let Q = 100, then R = 120% of 100 = 120 & P =125% of 120 = 150 So, P:Q:R = 15:10:12
Now, 15 + 10 + 12 = 37 units = Rs. 3330
Or 1 unit = Rs. 90
So, P = 15 units = 15 × 90 = Rs. 1350
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FAQs on Previous Year Topic Wise Questions With Solutions: Ratio & Proportion - CSAT Preparation - UPSC
| 1. What is the definition of ratio and proportion in mathematics? |  |
Ans.Ratio is a comparison between two or more quantities, showing the relative sizes of the quantities. It is expressed as a fraction or using a colon, such as 2:3 or 2/3. Proportion, on the other hand, states that two ratios are equal, indicating a relationship between the quantities. It can be expressed in the form a/b = c/d, where a, b, c, and d are numbers.
| 2. How can ratios be simplified, and why is it important? | |
Ans.Ratios can be simplified by dividing both terms of the ratio by their greatest common divisor (GCD). This simplification is important as it makes the ratio easier to understand and use in calculations. For example, the ratio 8:12 can be simplified to 2:3 by dividing both terms by 4, the GCD of 8 and 12.
| 3. What is the relationship between ratios and fractions? | |
Ans.Ratios and fractions are closely related concepts in mathematics. A ratio can be expressed as a fraction, where the first quantity is the numerator and the second is the denominator. For instance, the ratio 3:4 can be written as the fraction 3/4. Conversely, any fraction represents a ratio of two numbers, indicating how many parts of one quantity there are in relation to another.
| 4. How do you solve problems involving direct and inverse proportions? | |
Ans.In direct proportion, as one quantity increases, the other also increases at a constant rate. To solve these problems, you can set up the equation y = kx, where k is a constant. In inverse proportion, as one quantity increases, the other decreases. The relationship can be expressed as xy = k. To solve these, rearrange the equations based on the given values to find the unknown.
| 5. Can you provide an example of a real-world application of ratios and proportions? | |
Ans.Ratios and proportions are widely used in various real-world scenarios, such as cooking and mixing ingredients. For instance, if a recipe requires a ratio of flour to sugar of 3:1, and you want to make a larger batch, you can use proportions to determine how much sugar you need if you have 9 cups of flour. By setting up the proportion 3/1 = 9/x, you can solve for x, which would be 3 cups of sugar.
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