Question

The mean of 6 numbers is 20. If one number is deleted, their mean is 15. Find the deleted
number​

Answer 1

Answer:

Step-by-step explanation:

20  =   a + b + c + d + e + f /6

a + b + c + d + e + f  = 120

15  =  a + b + c + d + e / 5

a +  b + c + d + e  = 75

we get  45 gone

Answer 2

GiveN:

• The mean of 6 numbers is 20. If one number is deleted, their mean is 15.

To FinD:

• The deleted number

Required Solution:

Mean of 6 numbers = 20

$\sf Let \: the \: 6 \: numbers \: be \: \bf x_1, x_2, x_3, x_4, x_5, x_6$

⠀

$\sf Now, Mean = \bf \: \dfrac{x_1 + x_2 + x_3 + x_4 + x_5 + x_6}{6}$

⠀

∴⠀⠀$\bf \:20 = \dfrac{x_1 + x_2 + x_3 + x_4 + x_5 + x_6}{6}$

∴⠀$\bf \: x_1 + x_2 + x_3 + x_4 + x_5 + x_6 = 120$

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Now, when one number is deleted, mean becomes 15.

⠀

∴ Let the deleted number be $\bf \: x_1$

Therefore, the mean of rest off numbers

⠀

$\sf➟⠀\: \: \:New \:mean = \bf \dfrac{x_1 + x_2 + x_3 + x_4 + x_5 + x_6}{5}$

$➟⠀\: \: \: \: 15 = \bf \dfrac{x_1 + x_2 + x_3 + x_4 + x_5 + x_6}{5}$

$➟\: \: \: \: 75 = \bf {x_1 + x_2 + x_3 + x_4 + x_5 + x_6}$

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Putting the value of equation (ii) in equation (i), we get,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf {x_1 + x_2 + x_3 + x_4 + x_5 + x_6} \: = 120 \\ \\ ➟ \: \: \: \: \: \: \: \: \: \: \: \: \bf {x_1 + (x_2 + x_3 + x_4 + x_5 + x_6} )\: = 120 \\ \\ ➟ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf \: x_1 + 75 \: \: = 120 \\ \\ \bf \: \: \: \: \: \: \: \: \: \: \: \: \: ➟ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x_1 \: \: = 120 - 75 = 45$

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⠀⠀⠀Hence, the deleted number was 45