Question

Find a two digit no. If it is 36 less than the no. Obtained by reversing it's digit. The sum of the digit is 12.

Answer 1

Appropriate Question :-

Find a two digit number, if it is 36 less than the number obtained by reversing it's digit. The sum of the digit is 12.

$\large\underline{\sf{Solution-}}$

Let assume that

Digit at unit place be x

Digit at tens place be y

So,

Number formed = 10y + x

Reverse number = 10x + y

According to first condition,

The two digit number is 36 less than the number obtained by reversing the order of digits.

$\rm \: 10y + x = 10x + y - 36$

$\rm \: 10y + x - 10x - y = - 36$

$\rm \: 9y - 9x = - 36$

$\rm \: - 9(x - y) = - 36$

$\rm\implies \:x - y = 4 - - - (1)$

According to second condition,

The sum of the digits of two digit number is 12.

$\rm\implies \:x + y = 12 - - - (2)$

On adding equation (1) and (2), we get

$\rm \: 2x = 16$

$\rm\implies \:x = 8$

On Subtracting the value of x in equation (2), we get

$\rm \: 8 + y = 12$

$\rm \: y = 12 - 8$

$\rm\implies \:y = 4$

So,

Two digit number = 10 × 4 + 8 = 40 + 8 = 48

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Alternative Method:- Using one variable

Let assume that

Digit at units place be x

Since, it is given that, sum of digits of two digit number is 12

So, digit at tens place be 12 - x

Thus,

Number formed = 10 × (12 - x) + x = 120 - 10x + x = 120 - 9x

Reverse number = 10 × x + 12 - x = 10x + 12 - x = 12 + 9x

According to statement,

The two digit number is 36 less than the number obtained by reversing the order of digits.

$\rm \: 120 - 9x = 12 + 9x - 36$

$\rm \: 120 - 9x = 9x - 24$

$\rm \: - 9x - 9x = - 120 - 24$

$\rm \: - 18x = - 144$

$\rm\implies \:x = 8$

Hence,

Number formed = 120 - 9x = 120 - 9 × 8 = 120 - 72 = 48

Answer 2

QUESTION :

• Find a two digit no. If it is 36 less than the no. Obtained by reversing it's digit. The sum of the digit is 12.

GIVEN :

• is 36 less than the no. Obtained by reversing it's digit

• sum of the digit is 12

TO FIND :

• Find a two digit no = ?

SOLUTION :

we will assuming the a and b value :

forming the number = 10 b + a

reversing the number= 10 a + b

let us do it :

• 10b + a = 10a + b - 36

• 10b + a - 10a - b = -36

• 9 b - 9 a = - 36

• -9 ( a - b) = - 36

• a - b = 4

then, we have to find the number 12 :

• = a + b = 12

add the number we have :

• 2 a = 16

then, we will multiply 2 × 8 we get :

• a = 8

then, we have :

• 8 + b = 12

then, we will minus 12 with 8 we get :

• b = 12 - 8

• b = 4

then, we will 10 multiply with 4 and add with 8 we get :

• 40 + 8 = 48

so, we have two digit number = 48

then, we will do one extra Question like

this :

QUESTION :

• The sum of the digits of a two-digits number is 12. If the number formed by reversing the digits is less than the original number by 54, find the original number.

GIVEN :

• sum of the digits of a two-digits number is 12.

• less than the original number by 54

TO FIND :

• find the original number = ?

SOLUTION :

first digit = x

second digit = y

• x + y = 12

• 10 x + y - original

• 10 y + x

then, we have to do it :

• 10x + y - 54 = 10y + x

• 10x - x - 5y = 10y - y

• 9x - 54 = 9y

• 9x - 9y = 54

divide by 9 :

x - y = 6 - ( ii)

• x + y = 12

• x - y = 6

• 2 x = 18

then, we will divide 18 with 2 we get :

• x = 18 /2

put x = 9 in ( i) equation :

• 9 + y = 12

• y = 12 - 9 = 3

first digit = x = 9

second digit = y = 3

now original number = 90 + 3 = 93

• 93 - 54 = 39

• x+ y = 12 , 9 + 3 = 12