## The sum of a two digit number and the number formed by reversing the order of digit is 66 if the two digits differ by 2, find the number by

Question

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## Answers ( )

AnsweR:2 NUMBERS which are 24 and 42 .

ExplanatioN:Given:–ToFind:–SolutioN:–Let the First digit of the Original Number be

xand the Second digit bey.→ According to the First Condition :-

⇒ 10x + y + (10y + x) = 66

⇒ 10x + y + 10y + x = 66

⇒ 10x + x + 10y + y =66

⇒ 11x + 11y = 66

⇒ 11(x + y) = 66

⇒ x + y = 66 ÷ 11

⇒ x + y = 6 ———-

(1)→ According to the Second Condition :-

⇒ x – y = 2

⇒ x = y + 2 ————

(2)

⇨ Putting the Value of ‘x’ from Equation(2) in Equation(1) :-➟ (y + 2) + y = 6

➟ y + y + 2 =6

➟ 2y = 6 – 2

➟ 2y = 4

➟ y = 4 ÷ 2

➟

y = 2⇨ Now putting this value of ‘y’ in Equation(2) :-➠ x = 2 + 2

➠

x = 4So , we have the two digits as 4 and 2 .

∴ 2 Numbers can be formed from these 2 digits which are 42 and 24 .