The sum of the digits of a two digit number is 9. The number obtained by interchanging its digits is 9 less than thrice the original number. Find the no.
Answers
27
Step-by-step explanation:
Let the digit in the unit place be x and ten's place be y.
Hence, sum of the digits will be
→ x + y = 9 ...[1]
And original number,
→ 10y + x
Now the question states that the number obtained by interchanging it's digits is 9 less than thrice the original number.
Number after interchanging the digits ,
→ 10x + y
9 less than thrice the original number = Number after interchanging the digits
→ 3(10y + x) - 9 = 10x + y
→ 30y + 3x - 9 = 10x + y
→ 30y - y - 9 = 10x - 3x
→ 29y - 9 = 7x
→ -7x + 29y = 9 ...[2]
Multiplying [1] by 7
7(x + y = 9) → 7x + 7y = 63 ...[3]
Adding [2] and [3]
→ 7x + 7y + (-7x + 29y) = 9 + 63
→ 7x + 7y -7x + 29y= 72
→ 36y = 72
→ y = 72/36
→ y = 2
From [1]
→ x + y = 9
Substituting the value of y in the eq.
→ x + 2 = 9
→ x = 9 - 2
→ x = 7
Unit digit = x = 7
Ten's digit = y = 2
Hence, the number is 27.