Question

The difference between the tens and the units digits of


a two-digit number is 3. If the digits are interchanged


and the number is added to

the original number, we
get 121. What is the original


number?​

Answer 1

Answer :-

• Let the unit place be 'x' and tens place be 'y' in the original number.

Here 'x' and 'y' are variables.

Now, by using the variables 'x' and 'y', the

Original Number = 10y + x and, Number after interchanging the digits

= 10x + y

Now according to the question,

✏ y - x = 3 .... (i)

✏ (10x + y) + (10y + x) = 121 .... (ii)

From equation (ii) , we get,

=> 10x + y + 10y + x = 121

=> 11x + 11y = 121

Dividing each term at both sides by 11, we get,

=> x + y = 11

=> x = 11 - y ...(iii)

Now from equation (i) and (iii), we get,

▶ y - x = 3

▶ y - ( 11 - y ) = 3 {from eq. (iii)}

▶ y - 11 + y = 3

▶ 2y - 11 = 3

▶ 2y = 3 + 11

▶ 2y = 14

▶ $y \: \: = \: \: \dfrac{14}{2}$

▶ y = 7

So we get the value of, y = 7.

Now by applying the value of y, in equation (iii), we get,

• x = 11 - y = 11 - 7 = 4

So, we get the value of, x = 4

Now,

▶ Original Number = 10y + x = 10(7) + 4

= 70 + 4 = 74

▶No. after interchanging the digits = 10x + y

= 10(4) + 7 = 40 + 7 = 47

Hence, Original Number = 74

★ Verification :-

In order to verify, these values of x and y, we must ensure them if they are correct by applying those values in the equations we formed.

From equation (i),

we get,

=> y - x = 3

=> 7 - 4 = 3 since, y = 7, x = 3

This equation satisfies with the values of x and y.

From equation (iii), we get,

=> x + y = 11

=> 4 + 7 = 11

This equation satisfies with the values of x and y.

Since both of the equation satisfies with values of 'x' and 'y'. Hence, our answer is correct.