Question

The digit at the ten’s place of a two digit number is four times that in the unit’s place. If the digits are reversed, the new number will be 54 less than the original number. Find the original number.

Answer 1

Hi there !

Here's your answer


Let the digit in units place be x
Digit in tens place = 4x

The number formed will be 10(4x) + x = 40x + x
= 41x _ _ _ _ (i)


Given,

If the digits are reversed, the new number will be 54 less than the original number.


So,

Digit in units place = 4x
Digit in tens place = x

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

By balancing the equation,
we have

14x + 54 = 41x

54 = 41x - 14x

54 = 27x

$x = \frac{54}{27}$
x = 2


So,

Digit in units place = x = 2
Digit in tens place = 4x = 4× 2 = 8

Thus ,

The number formed is 82.

Answer 2

Answer:

Let the Number at the units place be x.Tenth place = 4x

Then,

➳ Number = 10(x) + 4x

➳ Number = 10x + 4x

➳ Number = 14x

➳ Reversing Number = 10(4x) + x

➳ Reversing Number = 40x + x

➳ Reversing Number = 41x

According to Question now,

➳ 14x - 41x = -54

➳ -27x = -54

➳ x = -54/-27

➳ x = 54/27

➳ x = 2

Units place = x = 2

Tenths place = 4x = 4(2) = 8

Therefore,

Number = 10(8) + 2 = 80 + 2 = 82