Question

5. The digit at ones place of a 2-digit number is four times the digit at tens place. The
number obtained by reversing the digits exceeds the given number by 54. Find
the given number.
ined by
​

Answer 1

☆ Correct Question ☆

The digit at ones place of a 2-digit number is four times the digit at tens place. The number obtained by reversing the digits exceeds the given number by 54. Find the given number.

☆ Solution ☆

Given

• The digit at ones place of a 2-digit number is four times the digit at tens place. The number obtained by reversing the digits exceeds the given number by 54.

To Find

• The number.

Step-by-Step-Explaination

Let tens digit be x and ones digit be y.

So, number = 10x + y

The digit at ones place of a 2-digit number is four times the digit at tens place.

As per given condition,

⇒ y = 4x

As per given condition,

⇒ 10x + y + 54 = 10y + x

⇒ 10x - x + y - 10y = - 54

⇒ 9x - 9y = - 54

⇒ 9(x - y) = - 54

⇒ x - y = - 6

⇒ x = y - 6

Substitute value of y = 4x above

⇒ x = 4x - 6

⇒ -3x = - 6

⇒ 3x = 6

⇒ x = 2

Substitute value of x = 2 in y

⇒ y = 4(2)

⇒ y = 8

Therefore,

Number = 10x + y = 10(2) + 8 = 28

Answer 2

✦ Question :-

The digit at ones place of a 2-digit number is four times the digit at tens place. The

number obtained by reversing the digits exceeds the given number by 54. Find

the given number.

ined by

Answer :-

$\underline{\boxed{\textsf{Number = {\textbf{28 }}}}} \qquad\qquad \bigg\lgroup\bold{Correct \ Answer} \bigg\rgroup$

$\Large{\underline{\underline{\bf{GiVen:-}}}}$

The digit at ones place = 4x

The number at tens place be x.

$\Large{\underline{\underline{\bf{Find:-}}}}$

Find the Two digit number .

$\Large{\underline{\underline{\bf{Solution:-}}}}$

As according to the given :-

So, we consider

the number at tens place be x

let the number at one's place be 4x

Now ,

The number together will be 10 x + 1(4x) = 14x

 So , as we know the number exceeds the digits sum by 54

Reversed number = 10y + x

As per the question :--

$:\implies\pink{\tt{10x + y + 54 = 10y + x}}$

$:\implies\pink{\tt{ 10x - x + y - 10y = - 54</p><p>}}$

$:\implies\pink{\tt{9x - 9y = - 54}}$

$:\implies\pink{\tt{9(x - y) = - 54}}$

$:\implies\purple{\tt{x - y = - 6}}$

Now ,just substituting the values in the above equation :-

✦ x - 4x = - 6

✦ - 3x = - 6

✦ x = 2

$\therefore\underline{\boxed{\textsf{ x = {\textbf{2}}}}} \qquad\qquad \bigg\lgroup\bold{the \ number \ at \ tens' place} \bigg\rgroup$

Now , simply by putting the value of x we get our value of y .

✦ y = 4x

✦ y = 4 × 2

✦ y = 8

From this :-

The digit at ones place = 4x = 8

The digit at tens place = x = 2

Hence ,

The no is 10 x + (y)

= 10 × 2 + ( 8 )

= 20 + 8

= 28 is the number .