CUET UG 2025 — General Test Quantitative Reasoning

Given $6x - 10y = 10$6x−10y=10 and $\frac{x}{x+y} = \frac{5}{7}$x+yx​=75​, we need to find $(x-y)$(x−y).

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Starting with the second equation:

$$\frac{x}{x+y} = \frac{5}{7}$$x+yx​=75​

$$7x = 5(x+y)$$7x=5(x+y)

$$7x = 5x + 5y$$7x=5x+5y

$$2x = 5y$$2x=5y

$$x = \frac{5y}{2}$$x=25y​

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Substituting $x = \frac{5y}{2}$x=25y​ into the first equation:

$$6\left(\frac{5y}{2}\right) - 10y = 10$$6(25y​)−10y=10

$$\frac{30y}{2} - 10y = 10$$230y​−10y=10

$$15y - 10y = 10$$15y−10y=10

$$5y = 10$$5y=10

$$y = 2$$y=2

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Finding the value of $x$x:

$$x = \frac{5y}{2}$$x=25y​

$$x = \frac{5(2)}{2}$$x=25(2)​

$$x = 5$$x=5

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Therefore:

$$x - y = 5 - 2 = 3$$x−y=5−2=3

The answer is $3$3.