a nber consists of two digits whose whose sum is 9 if 27 is subtracted from the number it's digits are in the reversed find the number
Answers
Answer :
›»› The Reversed number = 46
›»› The Original number = 63
Given :
- A number consists of two digits whose whose sum is 9 if 27 is subtracted from the number it's digits are in the reversed.
To Find :
- Reversed number = ?
- Original number = ?
Required Solution :
Here in this question we have to find Reversed number and Original number. So, firstly we have to assume the tens digit as an variable, accordingly to other one, after that we will find Reversed number and Original number on the basis of conditions given above.
Let ,
The tens digit be "x"
Then, the ones digit be "y"
- Original number = 10x + y
- Sum of two digit number = 9
→ x + y = 9 .....①
⪼ 27 is subtracted from the number it's digits are in the reversed.
→ Reversed number = 10y + x
→ 10x + y - 27 = 10y + x
→ 10x - x + y - 10y = 27
→ 9x - 9y = 27
→ 9(x - y) = 27
→ x - y = 27/9
→ x - y = 3 .....②
❒ Adding equation ① and equation ②,
→ x + y + x - y = 9 + 3
→ 2x = 12
→ x = 12/2
→ x = 6
❒ Put the value of x in equation ①
→ x + y = 9
→ 6 + y = 9
→ y = 9 - 6
→ y = 3
Now ,
→ Tens digit = x
→ Tens digit = 6
→ Ones digit = y
→ One digit = 3
Therefore ,
→ Reversd number = 10y + x = 96
→ Reversd number = 10 × 3 + 6
→ Reversd number = 30 + 6
→ Reversd number = 36
→ Original number = 10x + y = 69
→ Original number = 10 × 6 + 3
→ Original number = 60 + 3
→ Original number = 63
║Hence, the Reversed number is 36 and Original number is 63.║
Correct Question:
A number consists of two digits whose sum is 9. If 27 is subtracted from the number it's digits are reversed. Find the number.
Solution:
Let the unit's place digit be “x” and let the tenth place digit be “y”. Then,
The number is 10y + x.
Now According to the question,
x + y = 9
➝ x = 9 – y .....(i)
➝ 10y + x – 27 = 10x + y
➝ 10y – y + x – 10x = 27
➝ 9y – 9x = 27
➝ 9(y – x) = 27
➝ y – x = 27/9
➝ y – x = 3 ....(ii)
➝ y – (9 – y) = 3
➝ y – 9 + y = 3
➝ 2y = 3 + 9
= 12
➝ y = 12/2 = 6
Hence, y = 6
Now keeping the value of y in equation 1 we get,
x = 9 – y
= 9 – 6 = 3
Number = 10y + x
= 10 × 6 + 3
= 60 + 3 = 63
Hence, the number is 63.