Question

The peculiar number
There is a number which is very peculiar. This number is three times
the sum of its digits. Can you find the number?​

Answer 1

Answer:

Number is 27

$\rule{100}2$

Step-by-step explanation:

Let the number be 10M + N

In question it is not given that it is a one digit number, two digit number... and so on.

We assume it to be a two digit number.

Now,

According to question,

This number is three times the sum if it's digits.

Means, 10M + N is thrice (three times) the sum of it's digit (M and N).

i.e.

$\implies\:\sf{10M\:+\:N\:=\:3(M\:+\:N)}$

$\implies\:\sf{10M\:+\:N\:=\:3M\:+\:3N}$

$\implies\:\sf{10M\:-\:3M\:=\:3N\:-\:N}$

$\implies\:\sf{7M\:=\:2N}$

$\rightarrow\:\sf{M\:=\:\frac{2N}{7}}$ and $\sf{N\:=\:\frac{7M}{2}}$

Here, M is integer and N is multiple of 7. Similarly, N is integer and M is multiple of 2.

So,

$\implies\:\sf{M\:=\:2}$ and $\sf{N\:=\:7}$

$\therefore\:\sf{Number\:=\:10M\:+\:N}$

$\rightarrow\:\sf{10(2)\:+\:7}$

$\rightarrow\:\sf{27}$

Answer 2

${\large\bf{\mid{\overline{\underline{Correct\:Question:-}}}\mid}}$

There is a peculiar two digit number which is three times the sum of its digits. find the number?

$\Large\underline{\underline{\sf{Given}:}}$

• A peculiar number whose sum of digits is three times the number ...

$\Large\underline{\underline{\sf{Solution}:}}$

_________________

$\textbf{Let the two digits Number be (10x+y)}$

A/q,

$10x + y = 3(x + y) \\ \\ \red\leadsto \: \green{10x + y = 3x + 3y} \\ \\ \red\leadsto \: \blue{10x - 3x = 3y - y} \\ \\ \red\leadsto \: 7x = 2y \\ \\ \red\leadsto \red{\large\boxed{\bold{ \frac{x}{y} = \frac{2}{7} }}} \\ \\ \textbf{hence the number will be} \\ \\ \red\leadsto \green{ 10x + y} = \pink{10 \times 2 + 7} = \red{27}$

$\large\underline\textbf{Hope it Helps You.}$