Question

The number obtained by reversing a two digit number is 18 more than the original number sum of its digits is 8. find the number.

Answer 1

SOLUTION :-

Given :-

• sum of the digits of the number is 8

• reversed number is greater by 18 than the original number

To Find :-

• the required number

Assumption :-

• Let the two digit number be 10a+b

Solving :-

⇢ According to the Question :-

⇒ a+b = 8

⇒ a = (8-b) ...(i)

⇢ According to the Question :-

⇒ (10a+b) + 18 = 10b+a

⇒ 10(8-b) +b +18 = 10b+(8-b) ...(from ...i)

⇒ 80-10+b+18 = 10b+8-b

⇒ 80+18-8 = 10b-b+10b-b

⇒ 90 = 18b

∴ b = 5

∴ a = 8-b = 8-5 = 3

Answer :-

• the required number is :-

⇒ 10a + b

⇒ 10(3) + 5

⇒ 30+5

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