Question

18
The sum of the digits of a 2-digit number is 11. The number obtained by
interchanging the digits exceeds the original number by 27. Find the number.pls give explanation also and I will mark brainliest also.​

Answer 1

Answer:-

The Required number is 47.

Explanation:-

Given:-

• Sum of the digits of the two digit number is 11.

• The number obtained by inter changing the digits exceeds the original number by 11.

To Find:-

• The Number.

Now,

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

Therefore the original number would be,

= (10×digit at ten's place)+(1×digit at one's place).

= (10 × x) + (1 × y).

= (10x) + (y).

= 10x + y.

So The Number Obtained by inter changing digits will be 10y + x.

So ATQ:-

↦ Sum of digit at ten's place and one's place = 11.

↦ x + y = 11.... eq(I).

Also,

↦ Reversed Number = Orginal Number+27.

↦ 10y + x = 10x + y + 27.

↦ 10y + y + x - 10x = 27.

↦ 9y - 9x = 27.

↦ 9(y - x) = 27.

↦ y - x = 27/9.

↦ y - x = 3.... eq(II).

So we get two relations between x and y and hence we can find out the value of x and y.

Therefore,

By adding eq(I) and eq(II) we get,

↦ (x + y) + (y - x) = 11 + 3.

↦ x + y + y - x = 14.

↦ 2y = 14.

↦ y = 14/2.

↦ y = 7.

So The value of y is 7.

By putting the value of y in eq(I) we get,

↦ x + y = 11.

↦ x + 7 = 11.

↦ x = 11 - 7.

↦ x = 4.

An Hence,

The Original number is,

= 10x + y.

= (10 × 4) + 7.

= 40 + 7.

= 47.

So the required original number is 47.