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.​

Answer 1

Given,

• In two digit number, the digits in ten's place is triple the digit in unit place.
• When 36 is added to the number then the digits interchange their place.

To Find,

• Two digit Number Solution,

$\Rightarrow \: Suppose \: the \: digit \: at \: the t \: en's \\ place \: be \: a$

And, Suppose the digit at the one's place be b

Therefore,

• Two Digit Number =10a+b

• Interchange Number r = 10b + a

According to the First Condition :•

• In two digit number, the digits in ten's place is triple the digit in unit place.

${\Rightarrow{ \boxed {b=3a }}}$

According to the Second Condition

$\Rightarrow10a+b+36=10b+a;$

$\Rightarrow10a+3a+36=10(3a)+a;$

$\Rightarrow13a+36=30a+a;$

$\Rightarrow13a+36=31a;$

$\Rightarrow13a-31a=-36;$

$\Rightarrow-18a=-36;$

$\Rightarrow a= 36 18;$

${\Rightarrow{ \boxed{ a=2}}}$

Now Put value of a in First Condition :Now Put value of a in First Condition :

$\Rightarrow b=3a;$

$\Rightarrow b=3(2);$

${ \Rightarrow { \boxed{ b=6}}}</p><p>$

Therefore,

two digit number = 10a + b = 10(2) +6 = 26

interchange number= 10b + a = 10(6)+2=62

$\rule{200}2$

Answer 2

ab is the number

b=3a

ab means 10a+b

10a+b+36=10b+a  (the digits interchange their places)

substitute 3a for b

10a+3a+36=10(3a)+a

10a+3a+36=30a+a

13a+36=31a

36=31a-13a

36=18a

a=36/18

a=2

b=3 + 2=6

the number is 26

check: 26+36=62

Hope it helps you.