Question

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

Answer 1

Step-by-step explanation:

Given:

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

To Find:

• The original number.

Solution:

Let the number in unit's place be x and the number in ten's place be y.

➤ According to the question,

• The original number will be = 10y + x

➤ Now,

The digit at tens place = 4 × digit at unit's place

So, y = 4x

If If 54 is subtracted from the number, the digits are reversed.

∴ 10y + x - 54 = 10x + y

$\implies$ 9y - 9x = 54

$\implies$ y - x = 6

$\implies$ 4x - x = 6

$\implies$ 3x = 6

$\implies$ x = 2

Since, y = 4x = 4 × 2 = 8

∴ The original number = 10y + x = 10 × 8 + 2 = 82.

➤ Final Result:

• The original number is 82.

Answer 2

Answer:

Original number = 82

Step-by-step explanation:

❒Let the number be = $x$ and $y$

❒The digit at unit place = $x$

❒The digit at ten's place = $y$

❒So,original number  = $10x+y$

$\bold{According\:to\:question,}$

First its ten's digit is 4 times the units place

$\hookrightarrow y = 4x$

If 54 is subtracted from the number the digits are reversed

$\hookrightarrow 10y+x - 54 = 10x+y$

$\hookrightarrow 9y - 9x = 54$

$\hookrightarrow y -x = 6$

$\hookrightarrow 4x - x = 6$

$\hookrightarrow 3x = 6$

$\hookrightarrow x = \frac{6}{3}$

$\hookrightarrow x =2$

$\hookrightarrow y = 4x$

We got x value = 2

$\hookrightarrow y = 4 \times 2 = 8$

$\red{:\longmapsto}{\underline{\boxed{x = 2 , y = 8}}$

$\bold{Original\:number = 10y +x = 10(8)+2=82}$

$\red{:\longmapsto}\orange{\boxed{\mathcal{ORIGINAL\:\:NUMBER = }82}}$