CUET UG 2025 — General Test Arithmetic

The average of $39$39 numbers is $17$17.

Each number undergoes the following transformations: multiplied by $12$12, then $16$16 is added, then divided by $11$11.

When the same operations are applied to all numbers in a set, the average changes in the same way.

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Starting with the original average of $17$17:

After multiplying by $12$12:

$$17 \times 12$$17×12

$$= 204$$=204

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After adding $16$16:

$$204 + 16$$204+16

$$= 220$$=220

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After dividing by $11$11:

$$\dfrac{220}{11}$$11220​

$$= 20$$=20

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The transformation can be expressed as:

New Average $= \dfrac{12 \times \text{Old Average} + 16}{11}$=1112×Old Average+16​

New Average $= \dfrac{12 \times 17 + 16}{11}$=1112×17+16​

New Average $= \dfrac{204 + 16}{11}$=11204+16​

New Average $= \dfrac{220}{11}$=11220​

New Average $= 20$=20

Therefore, the average of the new set of numbers is $20$20.