Question

Average of six numbers is 8. The seventh number that increases the average to 11 is

Answer 1

Answer:-

Given:

Average of 6 numbers = 8.

Let the sum of the six numbers be "x".

We know that,

Average = sum of observations/Number of observations.

→ x/6 = 8

→ x = 48

And,

If a number is added with the six numbers the average becomes 11.

Let the number added be "y".

Hence,

(x + y)/6 + 1 = 11

Putting the value of x and on cross multiplicating we get,

→ 48 + y = 11*7

→ 48 + y = 77

→ y = 77 - 48

→ y = 29

Hence, the number added is 29.

Answer 2

$\huge{\bold{\star{\fcolorbox{black}{lightgreen}{ANSWER}}}}⋆$

• The added number is 29.

$\huge{\bold{\star{\fcolorbox{black}{lightgreen}{EXPLANATION}}}}⋆$

$\blue{\bold{\underline{\underline{Given}}}}$

• Average of 6 numbers is 8

$\blue{\bold{\underline{\underline{Let}}}}$

• The sum of the six numbers = 'x'

$\blue{\bold{\underline{\underline{Formula}}}}$

$Average = \frac{Sum \: of \: observations}{Number \: of \: observations} </p><p></p><p>$

$\frac{x}{6} = 8</p><p>$

$= > x = 8 × 6</p><p>$

$=> x = 48$

$\blue{\bold{\underline{\underline{And}}}}$

• If a number is added with the six numbers the average becomes 11.

$\blue{\bold{\underline{\underline{Let}}}}$

• The added number = 'y'

Hence,

$\frac{x + y}{6 + 1} = 11$

$\blue{\bold{\underline{\underline{Putting \: the \: value \: of \: x \: and \: on \: cross \: multiplicating}}}}$

$48 + y = 11 \times 7$

$= > 48 + y = 77$

$= > y = 77 - 48$

$= > y = 29$

$\blue{\bold{\underline{\underline{Answer}}}}$

The added number = 29.