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

Answer:

the number is 26

Step-by-step explanation:

if we add 36 to 26, then we get 62 which is reverse of 26. also 6 is thrice of 2

Answer 2

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,

⇒Suppose the digit at the ten's place be a

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

Therefore,

• Two Digit Number = 10a + b
• Interchange Number = 10b + a

According to the First Condition :-

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

$\implies \boxed{\sf{b = 3a}}$

According to the Second Condition :-

$\implies \sf{10a + b + 36 = 10b + a}$

$\implies \sf{10a + 3a + 36 = 10(3a) + a}$

$\implies \sf{ 13a + 36 = 30a + a}$

$\implies \sf{13a + 36 = 31a}$

$\implies \sf{13a - 31a = - 36}$

$\implies \sf{-18a = -36}$

$\implies \sf{a = \dfrac{36}{18}}$

$\implies \boxed{\sf{a = 2}}$

Now Put value of a in First Condition :-

$\implies \sf{b = 3a}$

$\implies \sf{b = 3(2)}$

$\implies \boxed{\sf{b = 6}}$

Therefore,

$\boxed{\sf{\purple{Two \ Digit \ Number = 10a + b = 10(2) + 6 = 26}}}$

$\boxed{\sf{\red{Interchange \ Number = 10b + a = 10(6) + 2 = 62}}}$

$\rule{200}2$