The digits of a three-digit number are in AP and their sum is 15. The

1.	The digits of a three-digit number are in AP and their sum is 15. The numberby reversing the digits is 594 less than the original number. Findthe number.
Answer» a, b, c Let the common difference be d Let the numbers be: b - d, b, b + d b - d + b + b + d = 15 = b = 5 Now, 100c + 10b + a + 594 = 100a + 10b + c 100(b+d) + (b - d) + 594 = 100(b - d) + (b + d) 500 + 100d + 5 - d + 594 = 500 - 100d + 5 + d 198d = -594 d = -3 a = 5 - (-3) and c = 5 + (-3) Hence the original number is: 852

The digits of a three-digit number are in AP and their sum is 15. The numberby reversing the digits is 594 less than the original number. Findthe number.

Answer»

a, b, c

Let the common difference be d

Let the numbers be: b - d, b, b + d

b - d + b + b + d = 15

= b = 5

Now, 100c + 10b + a + 594 = 100a + 10b + c

100(b+d) + (b - d) + 594 = 100(b - d) + (b + d)

500 + 100d + 5 - d + 594 = 500 - 100d + 5 + d

198d = -594

d = -3

a = 5 - (-3) and c = 5 + (-3)

Hence the original number is: 852