Question

In a two-digit number, the units digit is four
times the tens digit. If 54 is added to the
number, the digits interchange their places.
Find the original number.​

Answer 1

Answer:

The original number is 28 .

Step-by-step explanation:

Let the digit at the tens place be t .

So , digit at ones place = 4t

A/Q , 10 × t + 4t + 54 = 10 × 4t + t

=> 14t + 54 = 41t

=> 54 = 27t

=> t = 2

Answer 2

Given :-

1. A two-digit number, the units digit is four times the tens digit.

2. If 54 is added to the number, the digits interchange their places.

To Find :-

The original number.

Solution

Let us assume that the unit's place of the number be 'x'.

Let us assume that the ten's place of the number be 'y'.

∴ The two digit number is , 10y + x $\longrightarrow$ (1)

It is also said in the question that , the units digit is four times the tens digit.

$\implies$ y = 4x $\longrightarrow$(2)

If 54 is added to the number, the digits interchange their places.

Now,

Number obtained by reversing the digits = 10x + y

$\implies$ 10y + x + 54 = 10x + y

$\implies$ (10x - x) + (y - 10y) = 54

$\implies$ 9x - 9y = 54.

(On Dividing Completely by 9 )

$\implies$ x - y = 6 $\longrightarrow$(3)

Putting value of y as 4x as  from (2) in (3)

$\implies$ x - 4x = 6

$\implies$ -3x = 6

$\implies$ x = -2

Now , let us put x = -2 in (2).

$\implies$ y = 4 ×-2

$\implies$ y = -8

The original number is = 10y + x

Putting ,

y = -8  and  x = -2

$\implies$ The original number = 10 × -8 + -2

$\implies$ The original number = -82

Let Us Verify

Let us see if we add 54 to -82 if it interchanges the number.

- 82 + 54 = -28

∵ the digits interchanged the answer is correct.