the sum of the digits of a two digit numbers 7. If the digits are reversed, the new number decreased by 2, equals twice the original number. find the number.
Answers
The original number is 25.
Step-by-step explanation:
Given:
The sum of the digits of a two digit numbers 7.
The digits are reversed, the new number decreased by 2, equals twice the original number.
To Find :
The original number.
Solution :
Consider the :
The digits as: x and y.
So, The original number be 10x + y.
Hence,
Sum of the digits = x + y = 7 [ Equation 1 ]
Given, reversing the digits means y in tenth place and x in unit place. So, the reversed number be : 10y + x
Also given : reversed number is decreased by 2 = twice original number
Now,
⇒ 10y + x - 2 = 2(10x + y)
⇒ 19x - 8y = -2 [ Equation 2 ]
After solving Equation 1 & 2 :
⇒ x = 2
⇒ y = 5
The original number is 10x + y = 10(2) + 5 = 25
The reversed number is 10y + x = 10(5) + 2 = 52
The reversed number 52, when decreased by 2, is 50 which is twice the original number 25.
Hence,
The original number is 25.