The number is 41
Step-by-step explanation:
In a two-digit number,
Assume that in the two digit number y is in the unit's place and
x is in the ten's place, then the number is xy and its value is 10x + y
∵ The sum of its digit is 5
∵ Its digits are x and y
∴ x + y = 5 ⇒ (1)
∵ The value of the number is 10x + y
∵ If 27 is subtracted from the number then placed of digits are
interchange
- That means if we subtract 27 from 10x + y, then x and y will
change their places so the number will be yx and its value
will be 10y + x
∴ 10x + y - 27 = 10y + x
- Add 27 to both sides
∴ 10x + y = 10y + x + 27
- Subtract x from both sides
∴ 9x + y = 10y + 27
- Subtract 10y from both sides
∴ 9x - 9y = 27 ⇒ (2)
Now we have a system of equations to solve it
Multiply equation (1) by 9 to eliminate y
∴ 9x + 9y = 45 ⇒ (3)
- Add equations (2) and (3)
∴ 18x = 72
- Divide both sides by 18
∴ x = 4
Substitute the value of x in equation (1) to find y
∵ 4 + y = 5
- Subtract 4 from both sides
∴ y = 1
∵ The number is xy
∴ The number is 41
The number is 41
Learn more:
You can learn more about the system of equations in brainly.com/question/6075514
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