## 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

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

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3 weeks 2021-08-20T19:17:17+00:00 2 Answers 0 views 0

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....

### 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....

Put the value of ‘x’ in equation 2)

9 –y –y = 5

9 –2y = 5

–2y = 5 –9

–2y = –4

y = 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

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

### Originalnumber:–

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