Question

7. If the mean of numbers 27 + x, 31 + x,89 + x, 107 + x, 156 + x is 82, then the mean of
130 + x, 126 + X, 68 + x, 50 + x, 1 + xis
A. 75
D. 80
B. 157
E. None of these

i​

Answer 1

Answer-

Option a) 75

$\rule{100}2$

Step-by-step explanation-

Mean = $\sf{\dfrac{Sum\:of\:all\:observations}{Total\:number\:of\:observations}}$

Given condition is, 27+x, 31+x, 89+x, 107+x, 156+x is 82.

Here, total number of observations is 5.

Substitute them in above formula

$\rightarrow\:\sf{\dfrac{27+x+31+x+89+x+107+x+156+x}{5}\:=\:82}$

$\rightarrow\:\sf{\dfrac{410\:+\:5x}{5}\:=\:82}$

$\rightarrow\:\sf{410\:+\:5x\:=\:82(5)}$

$\rightarrow\:\sf{410\:+\:5x\:=\:410}$

$\rightarrow\:\sf{5x\:=\:0}$

$\rightarrow\:\sf{x\:=\:0}$

Now, we have to find the mean of 130+x, 126+x, 68+x, 50+x, 1+x

Again, substitute them in the known formula

$\rightarrow\:\sf{\dfrac{130+x+126+x+68+x+50+x+1+x}{5}\:=\:Mean}$

$\rightarrow\:\sf{\dfrac{375\:+\:5x}{5}\:=\:Mean}$

From above calculations we have x = 0

$\rightarrow\:\sf{\dfrac{375\:+\:5(0)}{5}\:=\:Mean}$

$\rightarrow\:\sf{\dfrac{375\:+\:0}{5}\:=\:Mean}$

$\rightarrow\:\sf{\dfrac{375}{5}\:=\:Mean}$

$\rightarrow\:\sf{75\:=\:Mean}$

Answer 2

Correct option is A. (75)

Explanation :-

★ Given :-

Mean of numbers 27 + x, 31 + x, 89 + x, 170 + x and 156 + x is 82.

________________________

★ To Find :-

We have to find the mean of 130 + x, 126 + X, 68 + x, 50 + x and 1 + x.

_______________________

★ Solution :-

We know the formula to find the mean of the numbers.

Firstly, from the first one we will find the value of x. Then, we will put the value of x and find the mean of the second one.

$mean \: = \frac{sum \: of \: observations}{number \: of \: observations}$

82 = (27 + x + 31 + x + 89 + x + 170 + x + 156 + x)/5

82 = (410 + 5x)/5

82 * 5 = 410 + 5x

410 = 410 + 5x

410 - 410 = 5x

5x = 0

x = 0/5

x = 5

_______________________

Now, put value of x.

$mean \: = \frac{sum \: of \: observations}{number \: of \: observations}$

Mean = 130 + x + 126 + x + 68 + x + 50 + x + 1 + x/5

Mean = (375 + 5x)/5

Mean = 375 + 5(0)/5

Mean = 375/5

Mean = 75

Therefore, correct option is A. (75)

____________________

★ Verification :-

For verification put value of x and mean respectively. If they both are equal then they are verified.

75 = 130 + x + 126 + x + 68 + x + 50 + x + 1 + x/5

75 = (375 + 5x)/5

75 = 375 + 5(0)/5

75 = 375/5

75 = 75

L.H.S = R.H.S

Hence Proved