Question

A number has two digits. The digit at the tens place is four times the digit at
the ones place. If 54 is subtracted from the number, the digits are reversed.
Find the number

Answer 1

Answer:

Your answer is attached above !!

Answer 2

Answer:

➨ㅤThe number is 82

Step-by-step explanation:

✮ Question :-

A number has two digits. The digit at the tens place is four times the digit at the ones place. If 54 is subtracted from the number, the digits are reversed. Find the number

✮ Solution :-

Let the digit at unit place be x and at tense be y

According to the Question

${\bold{\bf{y \: \: = \: \: \: 4x}}}$

Original number = 10y + x

Reversed number = 10x + y

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$\\ {\bold{\bf{⟼ \: \: 10y \: + \: x \: - \: 54 \: = \: 10x \: + \: y}}}$

${\bold{\bf{⟼ \: \: \: 9y \: - \: 9x \: = \: 54}}}$

${\bold{\bf{⟼ \: \: \: 9(y \: - \: x) \: = \: 54}}}$

${\bold{\bf{⟼ \: \: \: y \: - \: x \: = \: \frac{54}{9}}}}$

${\bold{\bf{⟼ \: \: \: y \: - \: x \: = \: 6}}}$

${\bold{\bf{⟼ \: \: 4x \: - \: x \: = \: 6 \: \: \: \: \: \: \: \: \: \: \: \: because \:\: \: ( y = 4x)}}}$

${\bold{\bf{⟼ \: \: \: 3x \: = \: 6 }}}$

${\bold{\bf{⟼ \: \: \: x \: = \: \frac{6}{3}}}}$

$⟼ \: \: \: {\bold{\bf{\fbox{\pink{ x \: = \: 2}}}}}$

We know that, y = 4x

Therefore

$⟼ \: \: \: {\bold{\bf{\fbox{\pink{ y \: = \: 8}}}}}$

So the original number should be,

10y + x = 10 × 8 + 2

$⟼ \: \: \: {\bold{\bf{\fbox{\orange{ 82}}}}}$