A two-digit number is 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.
Answers
Given : A two-digit number is 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.
Solution:
Let the digit in the unit's place be x and the digit at the tens place be y.
Number = 10y + x
The number obtained by reversing the order of the digits is = 10x + y
ATQ :
Condition : 1
10y + x = 4(x + y)
10y + x = 4x + 4y
4x + 4y - 10y - x = 0
3x - 6y = 0
3(x - 2y) = 0
x - 2y = 0 ……………(1)
Condition : 2
(10y + x) + 18 = 10x + y
10x + y - 10y - x = 18
9x - 9y = 18
9(x - y) = 18
x - y = 18/9
x - y = 2 …………..(2)
On Subtracting equation (2) from equation (1), we obtain :
x - 2y = 0,
x - y = 2
(-) (+) (-)
------------------
-y = - 2
y = 2
On putting y = 2 in eq (1) we obtain :
x - 2y = 0
x - 2 × 2 = 0
x - 4 = 0
x = 4
Now, Number = 10y + x = 10 × 2 + 4 = 24
Hence, the number is 24.
Hope this answer will help you…
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General form of a two digit number:- 10x + y
Reversed number:- 10y + x
The digits here are: x, y
Equations formed:
• 4(x + y) = 10x + y
=> 4x + 4y = 10x + y
=> 3y = 6x
=> y = 2x ___(1)
• 10x + y + 18 = 10y + x
=> 9y - 9x = 18
=> 9(y - x) = 18
=> y - x = 2
Put (1):
=> 2x - x = 2
=> x = 2
y = 2x = 4
Number: 10x + y