Question

the tens digit of a two digit number is three times the ones digit the sum of the original number and the number obtained by reversing the digits is 132.what is the two digit number. plz give answer with full explanation​

Answer 1

Let the numbers of the two digits number be xy.

» Tens digit number is three times of one's digit number.

→ 10x = 3y

→ 10x – 3y = 0 [1]

» After reversing the digits of the two digit number.

→ 10y + x

→ (10x + y) + (10y + x) = 132

→ 11x + 11y = 132

→ x + y = 12 [2]

After Calculating both the Equations, we've got that

→ 13x = 36

→ x = 36/13

→ x + y = 12

→ 36/13 + y = 12

→ y = 12 – 36/13

→ y = (156–36)/13

→ y = 120/13

Hence,

The numbers are 36/13 and 120/14 Respectively.

Answer 2

Step-by-step explanation:

${\LARGE{\mathfrak{\underline{\purple{Question :→}}}}}$

The tens digit of a two digit number is three times the ones digit the sum of the original number and the number obtained by reversing the digits is 132. What is the two digit number.

${\LARGE{\mathfrak{\underline{\purple{Answer :→}}}}}$

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

Then original number should be 10y + x ...eq(1)

According to the Condition Given

• y = 3x
• Number obtained by reversing the digits = 10x + y...eq(2)
• Sum of original number and reversed number = 132

Add eq(1) and eq(2) ,

${\bold{\sf{: \: ⟹ \: \: \: \: \: 10y \: + \: x \: + \: 10x \: + \: y \: = \: 132}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: 11x \: + \: 11y \: = \: 132}}}$

Putting the value of y from eq(1),

${\bold{\sf{: \: ⟹ \: \: \: \: \: 11x \: + \: 11(3x) \: = \: 132}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: 11x \: + \: 33x \: = \: 132}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: 44x \: = \: 132}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: x \: = \: \frac{132}{44}}}}$

$: \: ⟹ \: \: \: \: \: {\bold{\mathfrak{\fbox{\pink{ x \: = \: 3}}}}}$

Hence the unit's digit is 3

Let's calculate the value of y,

${\bold{\sf{: \: ⟹ \: \: \: \: \: y \: = \: 3x}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: y \: = \: 3 \: (3)}}}$

$: ⟹ \: \: \: \: \: {\bold{\mathfrak{\fbox{\pink{ y \: = \: 9}}}}}$

Hence the original number is 93 and reversed number is 39

$\\ {\large{\sf{\underline{Let's \: verify \: the \: solution}}}}$

According to question,

${\bold{\sf{: \: ⟹ \: \: \: \: \: original \: number \: + \: reversed \: number \: = \: 132}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: 93 \: + \: 39 \: = \: 132}}}$