The sum of the digits of a two digit number is 9. If the digits are exchanged the new number obtain is 9 less than the three times of the original number. find the two digit number.
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Let the digit at tens place is 'y' and the digit at units place is 'x'.
So, the original number = 10y + x.
The number formed on interchanging the digits = 10x + y.
Given that sum of digits of a two digit number is 9.
= > x + y = 9. ------ (1)
Given that the number obtained is 9 less than the three times the original.
= > 10x + y = 3(10y + x) - 9
= > 10x + y = 30y + 3x - 9
= > 10x + y - 30y - 3x = -9
= > 7x - 29y = -9 ---------- (2)
On solving (1) * 7 & (2), we get
= > 7x + 7y = 63
= > 7x - 29y = -9
-----------------------
36y = 72
y = 2.
Substitute y = 2 in (1), we get
= > x + y = 9
= > x + 2 = 9
= > x = 7.
Therefore, the 2 digit number is 10y + x = 10(2) + 7 = 27.
Hope it helps!
siddhartharao77:
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