Question

The digit in the tens place of a two digit number is three times that in the units place. If the digits are
reversed the new number will be 36 less than the original number. Find the original number.​

Answer 1

Question :-

• The digit in the tens place of a two digit number is three times that in the units place. If the digits are reversed the new number will be 36 less than the original number. Find the original number.

Answer

Given :-

• The digit in the tens place of a two digit number is three times that in the units place.
• If the digits are reversed the new number will be 36 less than the original number.

To Find :-

• The original number.

Solution :-

Let digit at ones place be 'x'.

and digits at tens place be 'y'.

So, original number = 10y + x.

and Reverse number = 10x + y

★ Case - 1

The digit in the tens place of a two digit number is three times that in the units place.

⇛y = 3x .........[1]

★ Case - 2

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

⇛ Original number- Reverse number = 36

⇛ 10y + x - (10x + y) = 36

⇛ 10y + x - 10x - y = 36

⇛ 9y - 9x = 36

On dividing by 9, we get

⇛ y - x = 4

Put y = 3x from equation [1], we get

⇛ 3x - x = 4

⇛ 2x = 4

⇛ x = 2

Put x = 2 in equation [1], we get

⇛ y = 3 × 2 = 6

⇛ Original number = 10y + x = 10 × 6 + 2 = 62

Answer 2

Step-by-step explanation:

Question :-

• The digit in the tens place of a two digit number is three times that in the units place. If the digits arereversed the new number will be 36 less than the original number. Find the original number

Solution :-

• Step 1

Let the digit in the units place of original number be x.

Form the original number.

Since, the digit in the tens place of a two-digit number is three times that in the units place.

Then the digit at tens place is 3x.

So the two-digit number is

$10(3x) + x \\ = 30x + x \\ = 31x \: \: \: \: \: \: \: \: \:$

• Step 2

Form the number after reversing the digits.

Then units place digit of this number is 3x

And the digit at tens place is x.

So the resulting two-digit number will be

$10x + 3x \\ = 13x \: \: \: \: \:$

• Step 3

Apply the given condition.

Since, after the digits are reversed,

the new number will be 36 less than

the original number.

So, original number is equal to sum of new number and 36.

$31x = 13x + 36$

• Step 4

Subtract 13x from both sides of the equation.

$31x - 1 3x = 13x +36 - 13x$

$18x = 36$

• Step 5

Divide both sides of the equation by 18.

$\frac{18x}{18} = \frac{36}{18}$

$or \: x = 2$

The units digit is 2 and therefore the tens digit is 3 x 2 which is 6.

The number is 62.

Let's Check

On reversing of digits of the number we get is 26.

Difference between original number and

new number = 62 - 26 = 36 as given.