CUET UG 2025 — General Test Arithmetic

The boat travels 63 km downstream and then 63 km upstream. The total journey time is 10 hours.

Let the river flow at $x$x km/hr.

Downstream speed $= 15 + x$=15+x km/hr

Upstream speed $= 15 - x$=15−x km/hr

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Time taken downstream $= \dfrac{63}{15 + x}$=15+x63​ hours

Time taken upstream $= \dfrac{63}{15 - x}$=15−x63​ hours

Total time $= 10$=10 hours

$$\dfrac{63}{15 + x} + \dfrac{63}{15 - x} = 10$$15+x63​+15−x63​=10

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$$63\left[\dfrac{1}{15 + x} + \dfrac{1}{15 - x}\right] = 10$$63[15+x1​+15−x1​]=10

$$63\left[\dfrac{15 - x + 15 + x}{(15 + x)(15 - x)}\right] = 10$$63[(15+x)(15−x)15−x+15+x​]=10

$$63\left[\dfrac{30}{225 - x^2}\right] = 10$$63[225−x230​]=10

$$\dfrac{1890}{225 - x^2} = 10$$225−x21890​=10

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$$1890 = 10(225 - x^2)$$1890=10(225−x2)

$$1890 = 2250 - 10x^2$$1890=2250−10x2

$$10x^2 = 2250 - 1890$$10x2=2250−1890

$$10x^2 = 360$$10x2=360

$$x^2 = 36$$x2=36

$$x = 6$$x=6

Therefore, the rate of flow of the river is 6 km/hr.