the sum of the digit of a two digit is 7 the number obtained by interchanging the digits exceeds the original number by 27 find the number
Answers
#Answer :)
Let the first digit = x
Therefore second digit = 7 - x
Number = 10 × (7 - x) + 1 × x
>> 70 - 10x + x
>> 70 - 9x
On interchanging the digits, number becomes = 10 × x + 1 × (7 - x)
>> 9+7x
According to Question:
>> 9 + 7x - (70 - 9x) = 27
>> 9 + 7x - 70 + 9x = 27
>> 18x - 63 = 27
>> 18x = 27 + 63
>> x = 2
Therefore first digit = 2
Number = 10 × 2 + 1 × 5
>> 25
#Thankies :)
#Keep answering :)
Answer:
The number is 25
Step-by-step explanation:
Let,
- Units digit = x
- Tens digit = 7 - x
★ Original Number :
= 10 (7 - x) + x
= 70 - 10x + x
= 70 - 9x
★ The number interchanging :
= 10 (x) + (7 - x)
= 10x + 7 - x
= 9x + 7
___________________
★ According to the Question :
The number obtained by interchanging the digit exceed the original number by 27.
⇒ 70 - 9x + 27 = 9x + 7
⇒ 70 + 27 - 9x = 9x + 7
⇒ 97 - 9x = 9x + 7
⇒ 97 - 7 = 9x + 9x
⇒ 90 = 18x
⇒ x = 90/18
⇒ x = 5
Units digit = 5
___________________
• Tens digit = 7 - x
⇒ 7 - x
⇒ 7 - 5
⇒ 2
Tens digit = 2
The number = 25
Therefore, the number is 25