Question

In a two digit number. The units digit is thrice the tens digit. If 36 is added to the number, the digits interchange their place. Find the number.
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Answer 1

Answer:

The Orignal Number is 62.

Step-by-step explanation:

Given :

Units digits is thrice the tens digit

The digits interchange when - 36 is added

To find :

The number

Solution :

✯ $\textsf{\underline{\underline{Original Number,}}}$

Let the digits be -

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

⇒ 10(y) + 3y

⇒ 10y + 3y

⇒ 13y --------- (Orignal Number)

$\rule{300}{1.5}$

✯ $\textsf{\underline{\underline{Number with reversed digits,}}}$

Let the digits be -

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

⇒ 10(3y) + y

⇒ 30y + y

⇒ 31y --------- (Number with reversed digits)

$\rule{300}{1.5}$

✯ $\textsf{\underline{\underline{According to the question,}}}$

The number gets reversed when 36 is added to it.

⇒ 13y + 36 = 31y

⇒ 13y - 31y = - 36

⇒ 18y = 36

⇒ y = 36/18

⇒ y = 2

$\rule{300}{1.5}$

✯ $\textsf{\underline{\underline{Orignal Number,}}}$

⇒ 13y

⇒ 13(2)

⇒ 26

$\rule{300}{1.5}$

✯ $\textsf{\underline{\underline{Verification,}}}$

The units place should be thrice of the tens place,

⇒ 2 × 3 = 6

Units place is 6

Reversed digits are 62,

⇒ 26 + 36 = 62

⇒ 62 = 62

$\therefore$ The Orignal Number is 62.

Answer 2

Solution :

Let the digit at tens place be x and digit at ones place be y

Given that units digit is thrice the tens digit i.e.

$\sf \: y = 3x....(i)$

$\star \sf \: Original \: Number = 10x +y$

$\star \sf \: Interchanged \: Number = 10y +x$

According to the Question :

$\longrightarrow \sf \: 10x + y + 36 = 10y + x$

Putting the value of equation i)

$\longrightarrow \sf \: 10x + 3x + 36 = 10(3x)+ x$

$\longrightarrow \sf \: 13x + 36 = 30x+ x$

$\longrightarrow \sf \: 13x + 36 = 31x$

$\longrightarrow \sf \: 13x - 31x = - 36$

$\longrightarrow \sf \: 13x - 31x = - 36$

$\longrightarrow \sf \: - 18x = - 36$

$\longrightarrow \sf \: x = \cancel\dfrac{ - 36}{ - 18}$

$\longrightarrow \sf \red{\: x = 2}$

Putting the value of x = 2 in equation i)

$\sf \: y = 3 \times 2$

$\longrightarrow \red{\sf \: y = 6}$

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$\star \sf \: Original \: Number = 10(2)+6 = \boxed{ \sf \: 26}$

$\star \sf \: Interchanged \: Number = 10(6) +2 = \boxed{ \sf \: 62}$