Question

the digit in the tens place of a two digit number is thrice times that is the units place if the digits are reversed the new number will be 36 less than the original number find the original number step by step​

Answer 1

Given:-

• The digit in the tens place of a two digit number is thrice the digit at unit's place.
• If the digits are reversed the new number will be 36 less than the original number.

To Find:-

• What is the original number ?

Solution:-

Let the digit at ten's place be 'x' and the digit at unit's place be 'y'

• Number = 10x + y

❍ The digit at ten's place is thrice the unit's digit.

➠ x = 3y....❶

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

◆ Reversed Number = 10y + x

${\underline{\bf{According \: To \: Question:-}}}$

➠ 10x + y –36 = 10y + x

➠ 10x + y –10y –x = 36

➠ 9x –9y = 36

Take common '9' from both sides

➠ x –y = 4....❷

Put the value of 'x' from equation 1) in equation 2)

➠ 3y –y = 4

➠ 2y = 4

➠ y = $\sf{\cancel\dfrac{4}{2}}$

$\large{\underline{\underline{\bf{\star \: y = 2 \: \star}}}}$

Put the value of 'y' in equation 1)

➠ x = 3 $\times$ 2

$\large{\underline{\underline{\bf{\star \: x = 6 \: \star}}}}$

❒ NUMBER = 10x + y

❒ NUMBER = 10(6) + 2

❒ NUMBER = 60 + 2

❒ NUMBER = 62

Hence, the number formed is 62.

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Answer 2

Solution :-

Let the one's place digit be x

∴ Tens place digit be 3x

∵ We know, Digit = 10 × Ten's digit + One's digit

So,

➵ 10 × 3x + x

➵ 30x + x

➵ 31x

Now, according to question we have to reverse the position of one's and ten's place digit

So,

➵ 10 × x + 3x

➵ 10x + 3x

➵ 13x

Now, according to question

➽ 31x - 36 = 13x

➽ 31x - 13x + 36

➽ 18x = 36

➽ x = 36/18

➽ x = 2

So, we got the value of x as 2

Now, finding the number

➸ 10 × 3(2) + (2)

➸ 10 × 6 + 2

➸ 60 + 2

➸ 62

Thus, the number is 62