sum of two digits of a 2- digit number is 12. if the digits are reversed, the new number, so formed increase by 36. Find the number.
Answers
Answer:
48
Step-by-step explanation:
let one's place = y
ten's place = x
Number = 10x + y
Acc to question,
x + y = 12 ➡️1
When digits are reversed ,
New Number = 10y + x
Acc to question ,
New No. = Original no. + 36
10y + x = 10x + y + 36
9y - 9x = 36
y - x = 4 ➡️ eq2
Adding eq 1 and 2
2y = 16
y = 8 , Put in eq 1
x = 4
Number = 48
EXPLANATION.
Sum of two digits number is 12.
The digits get reversed the new numbers of our increases by 36.
As we know that,
Let the number be : x and y.
Original number : 10x + y.
Reversed number : 10y + x.
Sum of two digits number is 12.
⇒ x + y = 12. - - - - - (1).
The digits get reversed the new numbers of our increases by 36.
⇒ 10y + x = 10x + y + 36.
⇒ 10y - y + x - 10x = 36.
⇒ 9y - 9x = 36.
⇒ y - x = 4. - - - - - (2).
From equation (1) and equation (2), we get.
Adding both the equation, we get.
⇒ x + y = 12. - - - - - (1).
⇒ y - x = 4. - - - - - (2).
We get,
⇒ 2y = 16.
⇒ y = 8.
Put the value of y = 8 in equation (1), we get.
⇒ x + y = 12. - - - - - (1).
⇒ x + 8 = 12.
⇒ x = 12 - 8.
⇒ x = 4.
Original number : 10x + y.
10(4) + 8 = 48.
∴ Original number : 48.