Ex.16.2 Q1 Playing with Numbers Solutions - NCERT Maths Class 8

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Question

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

 Video Solution
Playing With Numbers
Ex 16.2 | Question 1

Text Solution

What is known?

A puzzled number

What is unknown?

Value of the alphabet i.e. \(y.\)

Reasoning:

If the sum of all digits of a number is equal to \(9,\) then the number is a multiple of \(9.\)

Steps:

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.

\[\begin{align} 8 + y &= 9\\ y &= 9 - 8\\ y &= 1 \end{align}\]

Therefore, \(y\) should be \(1\) only.

  
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