If abc is a three digit number, then the number abc - a - b - c is divisible by
(a) 9
(b) 90
(c) 10
(d) 11

Solution:

abc - a - b - c = 100a + 10b + c - a - b - c = 99a - 9b = 9(11a - b)

Hence abc - a - b - c is divisible by 9

The answer is (a)

✦ Try This: If abcd is a four digit number, then the number abcd - a - b - c - d is divisible by (a) 9, (b) 90, (c) 10, (d) 11

abcd = 1000a + 100b + 10c + d

abcd - a - b - c - d = 1000a + 100b + 10c + d - a - b - c - d = 999a - 99b - 9c

abcd - a - b - c - d = 9(111a - 11b - c)

Hence abcd - a - b - c - d is divisible by 9.

The answer is (a)

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 16

---

NCERT Exemplar Class 8 Maths Chapter 13 Problem 9

If abc is a three digit number, then the number abc - a - b - c is divisible by (a) 9, (b) 90, (c) 10, (d) 11

Summary:

If abc is a three digit number, then the number abc - a - b - c is divisible by 9.

---

☛ Related Questions:

• A six-digit number is formed by repeating a three-digit number. For example 256256, 678678, etc. Any . . . .
• If the sum of digits of a number is divisible by three, then the number is always divisible by (a) . . . .
• If x + y + z = 6 and z is an odd digit, then the three-digit number xyz is (a) an odd multiple of 3, . . . .