Question

A number consists of 2 digits. The sum of its digits is 12.The number obtained by interchanging the digits is 36 less than the given number. Find the number.

Answer 1

HI DEAR,

Let the number be 10x +y

x+y = 12....

10y + x +36 = 10x + y

9y - 9x = -36

x - y = 4..

x = 4+y....

4+y+y = 12

4+2y = 12

2+y = 6

y = 4

x = 8

number = 84

HOPE IT HELPS..

MARK BRAINLIEST..❤❤

Answer 2

GIVEN:

• A number consists of 2 digits. The sum of its digits is 12.
• The number obtained by interchanging the digits is 36 less than the given number.

TO FIND:

• Find the number ?

SOLUTION:

Let the digit at unit's place be 'y' and the digit at ten's place be 'x'.

Then,

✰ Number = 10x + y ✰

CASE:- ❶

✮ A number consists of 2 digits. The sum of its digits is 12.

$\large \bf{\star \: x + y = 12...1)\: \star}$

CASE:- ❷

✮ The number obtained by interchanging the digits is 36 less than the given number.

◇ Number obtained by reversing the digits = 10y + x

◇ Number obtained by reversing the digits = Original number - 36

$\rm{\dashrightarrow 10y + x = 10x + y - 36}$

$\rm{\dashrightarrow 36 = 10x + y -(10y + x)}$

$\rm{\dashrightarrow 36 = 10x + y - 10y - x }$

$\rm{\dashrightarrow 36 = 9x - 9y }$

Divide by '9' on both sides

$\large\bf{\star \: x - y = 4....2) \: \star}$

$\rm{\dashrightarrow x = 4 + y }$

Put the value of 'x' from equation 2) in equation 1)

$\rm{\dashrightarrow (4+y) + y = 12}$

$\rm{\dashrightarrow 4 + 2y = 12 }$

$\rm{\dashrightarrow 2y = 12-4}$

$\rm{\dashrightarrow 2y = 8 }$

$\rm{\dashrightarrow y = \cancel\dfrac{8}{2}}$

$\bf{\star \: y = 4 \: \star}$

Put the value of 'y' in equation 2)

$\rm{\dashrightarrow x - 4 = 4 }$

$\rm{\dashrightarrow x = 4 + 4 }$

$\bf{\star \: x = 8\: \star}$

Number = 10x + y

➣ Number = 10(8) + 4

➣ Number = 80 + 4

➣ ✯ Number = 84 ✯

❛ Hence, the number formed is 84 ❜

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