Sum of the digits of a two-digit number
is 5. When we interchange the digits, it is
found that the resulting new number is
less than the original number by 27.
What is the two-digit number?
Answers
GIVEN:
- Sum of the digits of a two-digit number is 5.
- When we interchange the digits, the resulting new number is less than the original number by 27.
TO FIND:
- What is the original number ?
SOLUTION:
Let the digit at ten's place be 'x' and the digit at unit's place be 'y'
✧ NUMBER = 10x + y
CASE:- 1)
✍ Sum of the digits of a two-digit number is 5.
According to question:-
➾ x + y = 5....❶
➾ x = 5 –y
CASE:- 2)
✍ When we interchange the digits, the resulting new number is less than the original number by 27.
✦ Reversed Number = 10y + x
✦ Reversed Number = Original Number –27
According to question:-
➾ 10y + x = 10x + y –27
➾ 27 = 10x + y –10y –x
➾ 27 = 9x –9y
Take common 9 from both sides
➾ 3 = x –y....❷
Put the value of 'x' from equation 1) in equation 2)
➾ 3 = 5 –y –y
➾ 3 = 5 –2y
➾ 3 –5 = –2y
➾ –2 = –2y
➾ y =
❬ y = 1 ❭
Put the value of 'y' in equation 1)
➾ x + 1 = 5
➾ x = 5 –1
❬ x = 4 ❭
◉ NUMBER = 10x + y
◉ NUMBER = 10(4) + 1
◉ NUMBER = 40 + 1
◉ NUMBER = 41
❝ Hence, the number formed is 41 ❞
______________________
Given : Sum of the digits of a two-digit number is 5. When we interchange the digits, it is found that the resulting new number is less than the original number by 27.
Solution :
Let the digits at tens place and ones place be x and 5 - x respectively.
Now interchange the digits: digit at one's place and tens place be x and 5 - x respectively.
☯
Hence the digit at tens place and ones place of the number are 1 and 5 - x = 5 - 1 = 4.
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