Question

The sum of digit of a two digits number is
17. On reversing its digits the new number
is 9 more than the original number. find the
number​

Answer 1

To FIND THE NUMBER

EXPLANATION.

• GIVEN

Sum of digit of two digit number = 17

x + y = 17 .... (1)

original number = 10x + y

reversing number = 10y + x

According to question,

on reversing it's digit the new number is 9 more than it's original number.

10y + x = 10x + y + 9

9y - 9x = 9

y - x = 1 .....(2)

From equation (1) and (2) we get,

2y = 18

y = 9

put y = 9 in equation (1) we get,

x + 9 = 17

x = 8

Therefore,

The number is = 10x + y

10( 8 ) + 9 = 89

THE NUMBER IS = 89

Answer 2

GIVEN:

• The sum of digit of a two digits number is 17.
• On reversing its digits the new number is 9 more than the original number.

TO FIND:

• What is the original number ?

SOLUTION:

Let the digit at unit's place be 'y' and that of the digit at ten's place be 'x'

• NUMBER = 10x + y

CASE:- 1)

❐ The sum of digit of a two digits number is 17.

According to question:-

➨ x + y = 17....❶

➨ x = 17–y

CASE:- 2)

❐ On reversing its digits the new number is 9 more than the original number.

◈ Number obtained by reversing the digits = 10y + x

◈ Number obtained by reversing the digits = Original number + 9

According to question:-

➺ 10y + x = 10x + y + 9

➺ –9 = 10x + y – 10y –x

➺ –9 = 9x –9y

➨ –1 = x–y....❷

Put the value of 'x' from equation 1) in equation 2)

➺ –1 = 17–y–y

➺ –1 – 17 = –2y

➺ –18 = –2y

➺ y = $\sf{\cancel\dfrac{-18}{-2}}$

➺ ★ y = 9 ★

Put the value of 'y' in equation 1)

➺ x + 9 = 17

➺ x = 17–9

➺ ★ x = 8 ★

• NUMBER = 10x + y
• NUMBER = 10(8)+9
• NUMBER = 80+9
• NUMBER = 89

❝ Hence, the number formed is 89 ❞

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