Question

The average of 9 numbers is 25. if the average of the first five numbers is 15 and the average of the last 5 numbers is 35, what is the fifth number?

Answer 1

SOLUTION

GIVEN

• The average of 9 numbers is 25.

• The average of the first five numbers is 15

• The average of the last 5 numbers is 35

TO DETERMINE

The fifth number

EVALUATION

Here it is given that the average of 9 numbers is 25

So the sum of 9 numbers

= 9 × 25

= 225

The average of the first five numbers is 15

So the sum of the first five numbers

= 5 × 15

= 75

Again the average of the last 5 numbers is 35

So the sum of last 5 numbers

= 5 × 35

= 175

Let x be the fifth number

So by the given condition

225 + x = 75 + 175

$\sf{ \implies \: 225 + x = 250}$

$\sf{ \implies \: x = 250 - 225}$

$\sf{ \implies \: x = 25}$

FINAL ANSWER

The fifth number = 25

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