Question

number whose sum of digit is 14 when reversed gets a number 36 lesser than itself the number is​

Answer 1

CORRECT QUESTION :-

The sum of digits of a two digit number is 14. The new number formed by reversing the digits is greater than the original number by 36. Find the original number.

SOLUTION :-

Let,

Digit in ten's place = x

Digit in one's place = y

Original number = 10x + y

According to the first condition,

$\longrightarrow\sf x+y = 14 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...............(1)$

According to the second condition,

$\longrightarrow\sf 10x+y+36 = 10y+x \\\\\longrightarrow 10-x+y-10y= - 36 \\\\\longrightarrow 9x-9y = -36 \\\\\longrightarrow x-y = -4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...............(2)$

Add eq(1) and eq(2),

$\longrightarrow\sf 2x= 10 \\\\\longrightarrow\bf x= 5$

Substitute the value of x in eq(1),

$\longrightarrow\sf 5+y= 14 \\\\\longrightarrow \bf y = 9$

Original number = 59

Answer 2

Correct Question :-

The Sum of digits of two digit Numbers is 14. The new Number formed by reversing the digits is greater than the orginal number by 36.

To FinD :-

• The Orginal Number.

CalculaTioN :-

Let Us take variables on the basis of The digits

Let,

• Tens place = x

• Ones place = y

From the Question,

• Orginal Number = 10x+y

From First Condition

• x + y = 14 ----(1)

According to the Second Condition.

• 10x + y + 36 = 10y + x

Making like variables to each other,

• 10 - x + y - 10y - 36

• 9x - 9y = -36

On further simplification

• x - y = -4 ---- ( 2 )

Adding Equation (1) + Equation (2)

• 2x = 10

• x = 5

We can Conclude that tens place will be 50

Substitute the value of x in Equation (1)

• x + y = 14

Since x = 5

• 5 + y = 14

• y = 9

Hence ones place is 9

We know,

• Tens place = 50

• Ones place value = 9

Orginal Number = 50 + 9 = 59

$\boxed{ \bf{ \red{orginal \: number = 59}{} }{} }{}$