Question

A number consists of two digits whose sum is 8. If 18 is added to the numb
its digits are reversed. Find the number.​

Answer 1

GIVEN:

• The sum of the digits of two digit number is 8.
• If 18 is added to the number its digits are reversed.

TO FIND:

• What is the original number ?

SOLUTION:

Let the digit at unit's place be 'y' and the digit at ten's place be 'x'

✧ NUMBER = 10x + y

CASE:- 1)

✏ The sum of the digits of two digit number is 8.

According to question:-

➛ x + y = 8....1)

➛ x = 8 –y

CASE:- 2)

✏ If 18 is added to the number its digits are reversed.

✧ REVERSED NUMBER = 10y + x

According to question:-

➛ 18 + 10x + y = 10y + x

➛ 10x + y –10y –x = –18

➛ 9x –9y = –18

Take 9 common from both sides

➛ x –y = –2...2)

Put the value of 'x' from equation 1) in equation 2)

➛ 8 –y –y = –2

➛ –2y = –2 –8

➛ –2y = –10

➛ y = $\sf{\cancel\dfrac{-10}{-2}}$

❛ y = 5 ❜

Put the value of 'y' in equation 1)

➛ x + 5 = 8

➛ x = 8 –5

❛ x = 3 ❜

◉ NUMBER = 10x + y

◉ NUMBER = 10(3) + 5

◉ NUMBER = 30 + 5

◉ NUMBER = 35

❝ Hence, the number formed is 35 ❞

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