Question

While finding out the average of 10, two digit numbers, the digits of one of the numbers got interchanged due to which the average of the numbers was 3.6 more than the original average. Find the difference between the digits of the number in which the digits got interchanged? Select one: O a. 4 O 6.2 O c5 O d. 7​

Answer 1

        $\text{\huge \bf \underline{Answer:}}$

        $\text{Let the digits of the number that got interchanged be }x \text{ and }y$

$\implies \text{The number} = 10x + y$

$\implies \text{The interchanged number} = 10y + x$

        $\text{Let the sum of the other 9 numbers be }S$

$\implies \text{Original Average} = \dfrac{S + 10x + y}{10} \text{ ------ (i)}$

$\implies \text{New Average} = \dfrac{S + 10y + x}{10} \text{ ------ (ii)}$

        $\text{It is given that the new average is 3.6 more than the original}$

$\implies \text{New Average} = \text{Original Average} + 3.6$

        $\text{From (i) and (ii)}$

$\implies \: \dfrac{S + 10y + x}{10} = \dfrac{S + 10x + y}{10} + 3.6$

$\implies \: \dfrac{S + 10y + x}{10} = \dfrac{S + 10x + y + 36}{10}$

$\implies \: S + 10y + x = S + 10x + y + 36$

$\implies \: S + 10y + x - S - 10x - y - 36 = 0$

$\implies \: 9y -9x- 36 = 0$

$\implies \: 9(y - x - 4) = 0$

$\implies \: y - x - 4 = 0$

$\implies \: y - x = 4$

  $\therefore \: \: \: \boxed{\boxed{\text{The difference between the digits}= 4}}$

Answer 2

Concept

Average is the arithmetic mean and is calculated by summing a group of numbers and  dividing by the number of those numbers

Given

We have given 10 numbers and the average of the number 3.6 when the digits interchanged.

Find

We are asked to determine the difference between the digits of the number in which the digits got interchanged

Solution

Let digit of one's place be x and digit of ten's place be 10y.

The two-digit number $=10y+x$

When the numbers got interchanged then, the two-digit number becomes $=10x+y$

Let the sum of other 9 numbers be S then ,

Original average $=\frac{S+10y+x}{10}$      .....(1)

New average $=\frac{S+10x+y}{10}$      .....(2)

It is given that new average is 3.6 more than the original average.

$New= Original+3.6$          .....(3)

Putting the values of equation (1) & (2) in equation (3) , we get

$\frac{S+10x+y}{10} =\frac{S+10y+x}{10} +3.6\\\\S+10x+y=S+10y+x+36\\\\9x-9y=36\\\\x-y=4$

Hence , the difference between the digits of the number in which the digits got interchanged is 4.

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