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
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Answers ( )
GIVEN:
TO FIND:
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 =
❮ 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 ❞
______________________
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