Question

the sum of the two digit number and the obtained reverse number is 88. if the difference of digit at the ten's place and that at unit's place is 6.find the digit at the ten's place of number.
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Answer 1

Solution :-

Let :-

Digit in ten's place = x

Digit in one's place = y

Two digit number = 10x + y

According to the first condition :-

$\longrightarrow \sf 10x+y+10y+x = 88 \\\\\longrightarrow (10x+x)(10y+y ) = 88 \\\\\longrightarrow 11x+11y = 88 \\\\\longrightarrow x+y= 8 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ........................(1)$

According to the second condition :-

$\longrightarrow \sf x-y = 6 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ........................(2)$

Adding eq (2) and eq (1) :-

$\longrightarrow \sf 2x= 14 \\\\\longrightarrow \bf x = 7$

Substitute the value of x in eq (1) :-

$\longrightarrow\sf 7+y=8 \\\\\longrightarrow \bf y = 1$

Two digit number = 71

Digit at ten's place= 7

Answer 2

$\red\bigstar$Answer:

• Digit at ten's place = 7

$\pink\bigstar$ Given:

• The sum of the two digit number and the obtained reverse number is 88.
• The difference of digit at the ten's place and that at unit's place is 6.

$\blue\bigstar$To find:

• Find the digit at the ten's place of a number

$\green\bigstar$ Solution:

Let the digit in ten's place be 'x' and digit in one's place be 'y'.

So the two digit number formed = 10x + y

( $\because$ value of digit at ten's place is 10 × x )

According to the question,

$\hookrightarrow$ 10x + y + 10y + x = 88

$\hookrightarrow$ 10x + x + 10y + y = 88

$\hookrightarrow$ 11x + 11y = 88

$\hookrightarrow$ x + y = 8 .....(i)

According to the second given condition,

$\hookrightarrow$ x − y = 6 .......(ii)

Let's add equation (i) and equation (ii),

$\hookrightarrow$ x + y + x - y = 8 + 6

$\hookrightarrow$ 2x = 14

(y got cancelled)

$\hookrightarrow$ $\boxed{\sf x \: = \: 7 \:}$

By substituting the value of x in equation (i),

$\hookrightarrow$ x + y = 8

$\hookrightarrow$7 + y = 8

$\hookrightarrow$ y = 8 - 7

$\hookrightarrow$ $\boxed{\sf y \: = \: 1 \:}$

$\therefore$ The two digit number obtained is 71 and the digit at one's place is 7.

$\red\bigstar$ Concepts Used:

• Assumption of unknown values

• Substitution of values

• Equation of expressions

• Addition of equations