PYQ Vault

Ratio, Proportion and Variation

CDS Maths. Try each one first, then open its answer.

Top 10 CDS PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 7 times: CDS 1 2020, CDS 2 2020, CDS 1 2021, CDS 2 2022, CDS 2 2023, CDS 1 2024, CDS 1 2026. This one: CDS 1 2026 See all 7 of this type

    13
    If x varies directly as y, then which of the following is/are correct ? I. (x2+y2)(x^2 + y^2) varies directly as y2y^2. II. (x3y4)\left(\frac{x^3}{y^4}\right) varies directly as y. Select the answer using the code given below :

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  2. Question 2

    This type asked 6 times: CDS 1 2017, CDS 2 2019, CDS 1 2023, CDS 2 2023, CDS 1 2024, CDS 1 2025. This one: CDS 1 2025 See all 6 of this type

    45
    The ratio of sum of two numbers to their difference is 5:15 : 1. What is the ratio of the sum of their squares to the difference of their squares ?

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  3. Question 3

    This type asked 4 times: CDS 1 2017, CDS 2 2022, CDS 2 2023, CDS 2 2025. This one: CDS 2 2025 See all 4 of this type

    55
    XX and YY are two alloys of copper (Cu) and zinc (Zn). Alloy XX is prepared by mixing Cu and Zn in the ratio 5:45 : 4, and alloy YY is prepared by mixing Cu and Zn in the ratio 5:135 : 13 respectively. If equal quantities of alloys XX and YY are melted to form a third alloy ZZ, then what is the ratio of Cu to Zn in ZZ ?

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  4. Question 4

    This type asked 4 times: CDS 1 2019, CDS 2 2020, CDS 2 2023, CDS 2 2024. This one: CDS 2 2024 See all 4 of this type

    6
    pp varies directly as (x2+y2+z2)(x^2 + y^2 + z^2). When x=1x = 1, y=2y = 2, z=3z = 3, then p=70p = 70. What is the value of pp when x=−1x = -1, y=1y = 1, z=5z = 5 ?

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  5. Question 5

    This type asked 4 times: CDS 2 2016, CDS 1 2019, CDS 1 2021, CDS 2 2024. This one: CDS 2 2024 See all 4 of this type

    66
    A question is given followed by two statements I and II. Consider the Question and the Statements and mark the correct option. Question : The ratio of PP's salary to QQ's salary is 6:56 : 5. How much is PP's expenditure ? Statement-I : The ratio of PP's saving to QQ's saving is 3:23 : 2 Statement-II : The ratio of PP's expenditure to QQ's expenditure is 1:11 : 1 Which one of the following is correct in respect of the above Question and the Statements ?

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  6. Question 6

    This type asked 4 times: CDS 2 2017, CDS 1 2018, CDS 1 2020, CDS 2 2022. This one: CDS 2 2022 See all 4 of this type

    31
    If a=3ba = 3b, 4b=5c4b = 5c, 6c=7d6c = 7d, then what is d+ad−a\dfrac{d + a}{d - a} equal to ?

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  7. Question 7

    This type asked 4 times: CDS 2 2019, CDS 2 2020, CDS 2 2021, CDS 2 2022. This one: CDS 2 2022 See all 4 of this type

    2
    If a+bb+c=c+dd+a\frac{a + b}{b + c} = \frac{c + d}{d + a} where a≠ca \ne c, then which one of the following is correct ?

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  8. Question 8

    This type asked 3 times: CDS 1 2024, CDS 2 2024, CDS 2 2026. This one: CDS 2 2026 See all 3 of this type

    25
    An alloy (X) of gold and silver is taken in the ratio 1 : 2 and another alloy (Y) of gold and silver is taken in the ratio 2 : 3. How many parts of X and Y must be taken to obtain a new alloy Z consisting of gold and silver in the ratio 4 : 7 ?

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  9. Question 9

    This type asked 3 times: CDS 1 2018, CDS 1 2021, CDS 1 2025. This one: CDS 1 2025 See all 3 of this type

    10
    A mixture of 100 L contains kerosene and turpentine oil in the ratio 3 : 2. What is the minimum quantity of kerosene in litres (whole number) that should be mixed in the mixture so that the resulting mixture has 20% of kerosene ?

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  10. Question 10

    Asked 2 times: CDS 2 2016*, CDS 1 2023 (* = numbers or wording changed that year) See all 2 times it was asked

    6
    A, B, C, D and E enter into a business. They invest money in the ratio 2 : 3 : 4 : 5 : 6. However, the time invested by them is in the ratio 6 : 5 : 4 : 3 : 2. If the profit distributed is directly proportional to time and money invested, then who receives the highest amount of profit?

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