Question

the sum of digit of two digit number is 15. if the number formed by reversing the digit is less than 9 by the original number find the number​

Answer 1

Given

The sum of digit of two digit number is 15. if the number formed by reversing the digit is less than 9 by the original number.

To find

Find the number

Solution

➥ Let the tens digit be x and ones digit be y

• Original number = 10x + y

★Sum of digit of two digit number is 15

• x + y = 15 ---(i)

★If the number formed by reversing the digit is less than 9 by the original number.

• Reversed number = 10y + x

➠ 10x + y = 10y + x + 9

➠ 10x - x + y - 10y = 9

➠ 9x - 9y = 9

➠ 9(x - y) = 9

➠ x - y = 1

➠ x = (y + 1) ----(ii)

Substitute the value of x in equation (i)

➠ x + y = 15

➠ (y + 1) + y = 15

➠ 2y + 1 = 15

➠ 2y = 14

➠ y = 14/2 = 7

Put the value of y in equation (ii)

➠ x = (y + 1)

➠ x = 7 + 1

➠ x = 8

Hence,

• Original number = 10x + y = 87
• Reversed number = 10y + x = 78

Answer 2

ANSWER.

• The sum of a digits of two digit Number is 15.If the Number formed by reversing the digit is less than 9 from the original.

Let the Ones place digit be x

Tens Digit = (15-x).

Original Number= x+10(15-x) = 150-9x.

Now,

Atq.

• After reversing the digits the tens place changes to ones place and Vice versa.

Ones digit becomes=(15-x)

Tens digit becomes= x

New Number= 10×x+(15-x)= 9x+15

Now,

(New Number)-(original Number)=9

(9x+15)-(150-9x)=9

9x+15-150+9x=9

18x-135=9

18x=144

x=$\huge\frac{\cancel{144}}{\cancel{18}}$

x=8

The original Number is-

Ones Digit=8

Tens Digit=7

Thus, The Original Number formed is 87.