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.

Answer 1

Hey there!


Here is the answer of your question.

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Answer =>


Let the tens digit in two digit number be x and once digit be y.

Thus, Number = 10x + y

According to the Question,

x = 4y -------------------------------eq(i)

Also,
10x + y - 54 = 10y + x
10x - x + y - 10y = 54
9x - 9y = 54
9(x - y) = 54

x - y = 6 ------------------------------eq(ii),

Putting eq(i) in eq(ii),

x - y = 6
4y - y = 6
3y = 6
y = 2

Putting y = 2 in eq(i),
x = 4y
x = 4 * 2
x = 8

Thus, Number = 10x + y
= 10(8) + 2
= 80 + 2
= 82

Thus, the two-digit number is 82.


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Hope this helps you!

Answer 2

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

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.