Question

The sum of two digit number is 15. The number obtained by inter changing the digits exceeds the given number by 9. Find the number

Answer 1

Answer:

the number is 78. It's sum will be 15

and the number obtained by interchanging the digits will be 87 that is 9 more than the given or original number

Answer 2

In order to solve the problems based on two digit numbers, we must remember the following points into consideration.

1. When tens and ones digits of a two digit number are given in terms of variables, we can form the number by writing the tens digit followed by the ones digit of the number.

For if the ones and tens digits of a number 7 and 4 respectively, the number will be 47.

⠀2. When the tens and ones digits of a two digit number are given in terms of variable, we can not form the number by writing the tens digit followed by the ones digit of the number.

For example if the ones and tens digit of a number are x and y respectively, the number will not be xy.

This is because yx = y × x and if, x = 7 and y = 4 the value of yx = 4 × 7 = 28

This is important to note that in arithmetic, 47 $\cancel{=}$ 74 $\cancel{=}$ 7 × 4 or 7 × 4 but in algebra yx = xy = x × y = y × x.

Therefore when the digits of a two digit number are given as algebraic terms we cannot form the number by writing the tens digit followed by the ones digit of the number.

In such cases we use the expanded notation method to form the number, that is;

A two digit number = 10 × (tens digit) + 1 × (ones digit)

Let us form the two digit number using notation method.

Let the ones digit is x and tens digit is 15 - x of the two digit number

As we know that a two digit number = 10 × tens digit + 1 × ones digit

Therefore, Number = 10 × (15 - x) + x = 150 - 10x + x = 150 - 9x

On interchanging the digits;

NEW NUMBER = 10 × x + (15 - x) = 10x - x + 15 = 9x + 15

NOW, NEW NUMBER > orginal number by 9

SO, 9x + 15 = 150 - 9x + 9 ⇒ 18x = 159 - 15 ⇒18x = 144 ⇒ x = 144/18 ⇒ x = 8

Therefore, in the given number ones digit is 8 and tens digit is (15 - 8) = 7

HENCE, the number is 78