# The average of 11 numbers is 18. Out of these 11 numbers, the average of 9 numbers is 17. If the ratio of the remaining two numbers is 2 : 3. What is

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The average of 11 numbers is 18. Out of these 11 numbers, the average of 9 numbers is 17. If the ratio of the remaining two numbers is 2 : 3. What is the smaller number?
1. 27
2. 18
3. 19
4. 20
5. 15

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Correct Answer - Option 2 : 18

Given:

The average of 11 numbers = 18

The average of 9 numbers = 17

The ratio of the remaining 2 numbers = 2 : 3

Calculation:

Total of the 11 numbers = 11 × 18

⇒ 198

Total of the 9 numbers = 9 × 17

⇒ 153

∴ Total of the remaining 2 numbers = 198 – 153

⇒ 45

Let the remaining two numbers be 2x and 3x.

∴ 2x + 3x = 45

⇒ 5x = 45

⇒ x = 9

∴ the smaller number = 2x

⇒ 2 × 9

⇒ 18

∴ the smaller number is 18.