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Chain of ratios A:B, B:C, ... combined to find a ratio or expression

This type of question, asked 4 times: CDS 2 2017, CDS 1 2018, CDS 1 2020, CDS 2 2022. All 4 questions below, oldest first.

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  1. Question 1

    CDS 2 2017

    42
    There are 350 boys in the first three standards. The ratio of the number of boys in first and second standards is 2 : 3, while that of boys in second and third standards is 4 : 5. What is the total number of boys in first and third standards ?

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  2. Question 2

    CDS 1 2018

    24
    If A:B=1:2A : B = 1 : 2, B:C=3:4B : C = 3 : 4, C:D=2:3C : D = 2 : 3 and D:E=3:4D : E = 3 : 4, then what is B:EB : E equal to?

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  3. Question 3

    CDS 1 2020

    9
    If ab=13\frac{a}{b} = \frac{1}{3}, bc=2\frac{b}{c} = 2, cd=12\frac{c}{d} = \frac{1}{2}, de=3\frac{d}{e} = 3 and ef=14\frac{e}{f} = \frac{1}{4}, then what is the value of abcdef\frac{abc}{def} ?

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  4. Question 4

    CDS 2 2022

    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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