Question

The digit at the ten's place of a two digit number is four times that in the unit's place. If the digits are reserved, the new number formed will be 54 more than the original number. Find the original number

Answer 1

Answer:

The answer original no.= 72

Answer 2

${\blue{\underline{\textsf{\textbf{Answer : }}}}}$

The number is 82.

${\purple{\underline{\textsf{\textbf{Explaination : }}}}}$

Let's assume

➩ The numbers are x(ten's digit) and y (ones digit)

Number formed :

➩ 10x + y

Reversing the digits :

➩ 10y + x

As it is told that x is 4 times y

So, x = 4y ...... (i)

According to the question,

$\sf : \implies \: (10x + y) - (10y + x) = 54 \\ \sf : \implies \: 10x + y - 10y - x = 54 \\ \sf : \implies \: 9x - 9y = 54 \\ \sf : \implies \:9( x - y) = 54 \\ \sf : \implies \: x - y = \frac{54}{9} \\ \sf : \implies \: x - y = 6 \\ { \underbrace{ \textbf{ \textsf{ From ..(i)}}}} \\ \sf : \implies \: 4y - y = 6 \\ \sf : \implies \: 3y = 6 \\ \sf : \implies \: y = \frac{6}{3} \\ \sf : \implies \: y = 2$

After solving we get :

➩ y = 2

And also,

x = 4y

x = 4*2

x = 8

Hence,

The number is :

➩ 10x + y

➩ (10*8) + (2)

➩ 80 + 2

➩ 82 ans.