Question

the sum of the digits of a two-digit
number is 4. The number got by isterchanging the digits is 18 less than the
original number. What is the bumber?​

Answer 1

★ Correct Question ★

• The sum of the digits of a two-digit number is 4. The number got by interchanging the digits is 18 $less$than the original number. What is the number?

★Given :-

• The sum of the digits of a two-digit number is 4.
• The number got by interchanging the digits is 18 less than the original number.

★ To Find :-

• What is the number?

★ Solution :-

Let we consider the numbers be :-

Digit in ten's place be ' x ' and digit in one's place be ' y ' respectively.

So, from given :- x + y = 4 ------ eq(1)

Then,

The number = 10x + y

Now, Digit are interchanged,

New interchanged number = 10y + x

Now, as per the question

• ( 10x + y) - ( 10y + x) = 18

➹ 10x + y - 10y - x = 18

➹ 9x - 9y = 18

➹ 9( x - y) = 18

➹ x - y = 18/9

➹ x - y = 2 ----- eq( 2)

Now, let's Add both the eq(1) and eq( 2 )

Then we get,

( x + y) + ( x - y) = 4 + 2

➹ 2x = 6

➹ x = 6/2

➹ x = 3

Using substitution method to find the value of 'x '

Putting the value of x in eq(1)

➹ x + y = 4

➹ 3 + y = 4

➹ y = 4 - 3

➹ y = 1

Therefore,

☆ The two digit number = 31

_________________________