Question

If the sum of the digits of a two digit number is 9 and the difference between the number and that formed by reversing the digits is 45 then number is A.81 B.72 C.45 D.54

Answer 1

GIVEN:

• Sum of the digits of a two digit number is 9
• Difference between the number and that formed by reversing the digits is 45

TO FIND:

• What is the original number ?

SOLUTION:

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

CASE:- 1)

✧ Sum of the digits of a two digit number is 9.

According to question:-

➸ x + y = 9

➸ x = 9 –y....❶

CASE:- 2)

✧ Difference between the number and that formed by reversing the digits is 45.

✦ Reversed Number = 10y + x

✦ Original Number – Reversed Number = 45

According to question:-

➸ 10x + y –(10y + x) = 45

➸ 10x + y –10y –x = 45

➸ 9x –9y = 45

Taking common 9 from both sides

➸ x –y = 5....❷

Put the value of 'x' in equation 2)

➸ 9 –y –y = 5

➸ 9 –2y = 5

➸ –2y = 5 –9

➸ –2y = –4

➸ y = $\sf{\cancel\dfrac{-4}{-2}}$

❮ y = 2 ❯

Put the value of 'y' in equation 1)

➸ x = 9 –2

❮ x = 7 ❯

◉ NUMBER = 10x + y

◉ NUMBER = 10(7) + 2

◉ NUMBER = 70 + 2

◉ NUMBER = 72

❝ Hence, the number formed is 72 ❞

______________________

Answer 2

Question:-

If the sum of the digits of a two digit number is 9 and the difference between the number and that formed by reversing the digits is 45 then number is

A) 81

B) 72

C) 45

D) 54

Answer:-

Original number:-

Let the digit in unit's place be x

Then the digit in ten's place will be (9 - x) [As the sum of digit is 9]

Hence, the number is 10(9 - x) + x = 90 - 9x

New reversed number:-

Digit in unit's place will be (9 - x)

Digit in ten's place will be x

Hence, the number is 10x + (9 - x) = 9x + 9

We know that,

Original number - new number = 45

=> 90 - 9x - (9x + 9) = 45

=> 90 - 9x - 9x - 9 = 45

=> -18x = -36

=> x = 2

Hence,

original number = 90 - 9x = 90 - 18 = 72

Ans. Original number = B) 72