A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:

Question: A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:Solution: let, the digits are x, y, z x + y + z = 10 y = x + zy + y = 10 ⇒ y = 5x + z = 5(100z + 10y + x) - (100x + 10y + z) = 99⇒ 99z - 99x = 99⇒ z - x = 1x + z + z - x = 5 + 1⇒ 2z = 6∴ z = 3x = 5 - 3 = 2The number is = 253