Sum of the digits of a two digit number is 9. When we interchange the digits, it is found that the resulting number is greater than the original number by 27. What is the two digit number?
Answers
Answer:
Let the digits of the original number be x and y
Hence, the original number is 10x + y (Assuming x to be the ten's digit and y to be the one's digit)
After interchanging the digits the new number will be 10y + x (After reversing, y becomes the ten's digit and x becomes the one's digit)
Condition 1: Sum of the digits is 9 ⇒ x + y = 9 --------- equation (i)
Condition 2: The number obtained by interchanging the digits is 27 greater than the earlier number.
⇒ New number = 27 + original number
⇒ 10y + x = 27 + (10x + y)
⇒ 10y + x = 27 + 10x + y
⇒ 10y - y + x - 10x = 27
⇒ 9y - 9x = 27
⇒ y - x = 3 -------- equation (ii)
By adding equation(i) and equation(ii):
x + y + y - x = 9 + 3
⇒ 2y = 12
⇒ y = 6
From equation(i): x + 6 = 9
⇒ x = 9 - 6 = 3
⇒ x = 3 and y = 6
⇒ The required number is 10x + y = 10 × 3 + 6 = 30 + 6 = 36
Thus, the required two-digit number is 36.
HOPE IT HELPS YOU ....:)
Answer:
why are you leaving unnie
do you use pin