Question

The digit in the tens place of two digit number is three times that in the unit place . if the digits are reversed, the new number will be 36 less than the original number. find the original number. check your solution​

Answer 1

Answer:

The Original Number is 62.

Step-by-step explanation:

Given :

Digits at tens place = three times that in the unit place.

Number with reversed Digits = 36 less than the original number.

To find :

The Original Number

Solution :

Let the Digits in Original Number be -

• Units = x
• Tens = 10(3x)

Original Number = 10(3x) + x

➙ 30x + x

➙ 31x .......... (Original Number)

$\rule{300}{1}$

Let the Number with Reversed Digits be -

• Units Place = 3x
• Tens Place = 10(x)

Number = 10(x) + 3x

➙ 10x + 3x

➙ 13x ......... (Number with Reversed Digits)

$\rule{300}{1}$

According to the Question -

Number with reversed Digits = 36 less than the original number.

➙ 13x = 31x - 36

➙13x - 31x = - 36

➙ - 18x = - 36

➙ x = 36/18

➙ x = 2

Units Place = 2

$\rule{300}{1}$

Tens Place =

➙ 3x

➙ 3(2)

➙ 6

$\rule{300}{1}$

Original Number =

➙Tens Place = 6 ; Units Place = 2

➙ 62

$\therefore$ The Original Number is 62.

$\rule{300}{1}$

Verification :-

Number with Reversed Digits of 62 is 26.

Check whether the Difference between both is 36 or not.

➙ 62 - 26

➙ 36

$\therefore$ The Original Number is 62.

Answer 2

Answer:

The Original Number is 62.

Step-by-step explanation:

Given :

The digit in the tens place of two digit number is = three times that in the unit place.

When the digits are reversed, the new number will be = 36 less than the original number.

To find :

The original number

Solution :

Original Number :

Consider the -

• Units Place as y
• Tens Place as 10(3y)

Number Formed = 10(3y) + y

➨ 30y + y

➨ 31y ..... [Original Number]

$\rule{300}{1.5}$

Number with Reversed Digits -

Consider the -

• Units Place = 3y
• Tens Place = 10(y)

Number Formed = 10(y) + 3y

➨ 10y + 3y

➨ 13y ..... [Number with Reversed Digits]

$\rule{300}{1.5}$

As given in the Question -

When the digits are reversed, the new number will be = 36 less than the original number.

➨ 13y = 31y - 36

➨ 13y - 31y = - 36

➨ - 18y = - 36

➨ 18y = 36 .... (Negative signs to be cancelled)

➨ y = 36/18

➨ y = 2

$\rule{300}{1.5}$

As we got the value of y, find the original number by placing the y's value.

➨ 31y

➨ 31(2)

➨ 62

Original number = 62

$\therefore$ The Original Number is 62.

$\rule{300}{1.5}$

Verification :-

Check if both (LHS & RHS) are equal or not.

➨ 13y = 31y - 36

➨ 13(2) = 31(2) - 36

➨ 26 = 62 - 36

➨ 26 = 26

➨ LHS = RHS

$\therefore$ The Original Number is 62.