CUET UG 2025 — General Test Arithmetic

Given that 10% of $X$X = 15% of $Y$Y = $\frac{1}{5}$51​ of $Z$Z.

Converting to fractions:

$$\frac{10}{100} \times X = \frac{X}{10}$$10010​×X=10X​

$$\frac{15}{100} \times Y = \frac{3Y}{20}$$10015​×Y=203Y​

$$\frac{1}{5} \times Z = \frac{Z}{5}$$51​×Z=5Z​

Therefore:

$$\frac{X}{10} = \frac{3Y}{20} = \frac{Z}{5}$$10X​=203Y​=5Z​

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Let each expression equal $k$k:

$$\frac{X}{10} = k$$10X​=k

$$\frac{3Y}{20} = k$$203Y​=k

$$\frac{Z}{5} = k$$5Z​=k

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Solving for $X$X, $Y$Y, and $Z$Z:

$$\frac{X}{10} = k$$10X​=k

$$X = 10k$$X=10k

$$\frac{3Y}{20} = k$$203Y​=k

$$3Y = 20k$$3Y=20k

$$Y = \frac{20k}{3}$$Y=320k​

$$\frac{Z}{5} = k$$5Z​=k

$$Z = 5k$$Z=5k

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The ratio is:

$$X : Y : Z = 10k : \frac{20k}{3} : 5k$$X:Y:Z=10k:320k​:5k

Multiplying by 3 to eliminate the fraction:

$$X : Y : Z = 30k : 20k : 15k$$X:Y:Z=30k:20k:15k

$$X : Y : Z = 30 : 20 : 15$$X:Y:Z=30:20:15

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Dividing by the common factor 5:

$$30 \div 5 = 6$$30÷5=6

$$20 \div 5 = 4$$20÷5=4

$$15 \div 5 = 3$$15÷5=3

Therefore, $X : Y : Z = 6 : 4 : 3$X:Y:Z=6:4:3