CUET UG 2025 — General Test Quantitative Reasoning

Let the first part be $x$x and the second part be $y$y.

The two parts must add up to 26:

$$x + y = 26$$x+y=26

The problem states that three times the first part and seven times the second part equals 122:

$$3x + 7y = 122$$3x+7y=122

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From the first equation, express $x$x in terms of $y$y:

$$x = 26 - y$$x=26−y

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Substitute into the second equation:

$$3(26 - y) + 7y = 122$$3(26−y)+7y=122

$$78 - 3y + 7y = 122$$78−3y+7y=122

$$78 + 4y = 122$$78+4y=122

$$4y = 122 - 78$$4y=122−78

$$4y = 44$$4y=44

$$y = 11$$y=11

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Substitute back to find $x$x:

$$x = 26 - y$$x=26−y

$$x = 26 - 11$$x=26−11

$$x = 15$$x=15

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The ratio of the first part to the second part is:

$$x : y = 15 : 11$$x:y=15:11

Therefore, the ratio of the first and second part is $15:11$15:11.