Question

A three digit number is such that the sum of its digits is 17. The middle digit of the number is 6 if 297 is subracted from the number, the hundreds digit and the unit digit of the number are interchanged. find the number.

Answer 1

Let the three digit number be x6y. (As middle digit is given)
Its numerical value is 100x + 60 + y.
Number formed by reversing its digits is y6x.
Its numerical value is 100y + 60 + x
⇒ x + 6 + y = 17 (given)
⇒ x + y = 11 → (i)
Also, 100x + 60 + y – 297 = 100y + 60 + x
⇒ 99x - 99y = 297
⇒ x - y = 3 → (ii)
Add equations (i) and (ii), we get
x + y = 11
x – y = 3
2x = 14 ⇒x = 7
From equation (i),
⇒ (7) + y = 11 ⇒ y = 4.
∴ The number is 764.