CUET UG 2025 — General Test Arithmetic

The given ratios are $a:b = \frac{12}{5}:\frac{3}{10}$a:b=512​:103​ and $b:c = \frac{7}{9}:\frac{12}{7}$b:c=97​:712​.

To simplify $a:b = \frac{12}{5}:\frac{3}{10}$a:b=512​:103​:

$$\frac{a}{b} = \frac{12/5}{3/10}$$ba​=3/1012/5​

$$\frac{a}{b} = \frac{12}{5} \times \frac{10}{3}$$ba​=512​×310​

$$\frac{a}{b} = \frac{120}{15}$$ba​=15120​

$$\frac{a}{b} = 8$$ba​=8

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To simplify $b:c = \frac{7}{9}:\frac{12}{7}$b:c=97​:712​:

$$\frac{b}{c} = \frac{7/9}{12/7}$$cb​=12/77/9​

$$\frac{b}{c} = \frac{7}{9} \times \frac{7}{12}$$cb​=97​×127​

$$\frac{b}{c} = \frac{49}{108}$$cb​=10849​

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To find $a:c$a:c:

$$\frac{a}{c} = \frac{a}{b} \times \frac{b}{c}$$ca​=ba​×cb​

$$\frac{a}{c} = 8 \times \frac{49}{108}$$ca​=8×10849​

$$\frac{a}{c} = \frac{392}{108}$$ca​=108392​

$$\frac{a}{c} = \frac{98}{27}$$ca​=2798​

Therefore, $a:c = \dfrac{98}{27}$a:c=2798​