Question

A number has two digits. the digit at ten's place is four times the digit at unit place. if 54 is subtracted from the number, the digits become reserved. find the number. please give the answer.

Answer 1

hi

let the number be xy

tens place = 10x 

ones place  = y

the digit at ten's place is four times the digit at unit place

so x = 4y..[1]

if 54 is subtracted from the number, the digits become reserved

10x +y - 54 = 10y +x.[2]

now lets put [1] in [2]


=>10x +y - 54 = 10y +x

=> 10(4y) + y -54 = 10y + 4y

.=> 41y - 54 = 14y

=>41y - 14y = 54

=> 27y = 54

=>y = 54/27

=>y = 2

since x = 4y

=> 2*4

=> 8

hence the number is xy

=>82

hope it helps u

:)

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.