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.

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