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# If 21y5 is a multiple of 9, where y is a digit, what is the value of y?

**Solution:**

We know that, according to divisibility rules, if the sum of all the digits of a number is equal to 9 or its multiples, then the number is a multiple of 9.

- If a number is a multiple of 9, then the sum of its digits will be divisible by 9.
- Sum of digits of 21y5 = 2 + 1+ y + 5 = 8 + y
- Hence, 8 + y should be a multiple of 9.
- This is possible when 8 + y is any one of these numbers 0, 9, 18, 27, and so on ...
- However, since y is a single-digit number, this sum can be 9 only.

8 + y = 9

y = 9 - 8

y = 1

Therefore, y should be 1.

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

**Video Solution:**

## If 21y5 is a multiple of 9, where y is a digit, what is the value of y?

Class 8 Maths NCERT Solutions Chapter 16 Exercise 16.2 Question 1

**Summary:**

If 21y5 is a multiple of 9, where y is a digit, the value of y should be 1.

**☛ Related Questions:**

- If 31z5 is a multiple of 9, where z is a digit, what is the value of z? You will find that there are two answers for the last problem. Why is this so?
- If 24x is a multiple of 3, where x is a digit, what is the value of x? (Since 24x is a multiple of 3, its sum of digits 6 + x is a multiple of 3; so 6 + x is one of these numbers: 0, 3, 6, 9, 12, 15, 18, ... . But since x is a digit, it can only be that 6 + x = 6 or 9 or 12 or 15. Therefore, x = 0 or 3 or 6 or 9. Thus, x can have any of four different values.)
- If 31z5 is a multiple of 3, where z is a digit, what might be the values of z?

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