Question

The sum of the digits of a two-digit number is 12. The number obtained by interchanging its digits exceeds the given number by 18. Find the number.

Answer 1

Let us consider, One’s digit of a two digit number = x and Ten’s digit = y So, the number is x + 10y By interchanging the digits, One’s digit = y and Ten’s digit = x Number is y + 10x As per the statement, x + y = 12 ………. (1) y + 10x = x + 10y + 18 y + 10x – x – 10y = 18 x – y = 2 …(2) Adding (1) and (2), we have 2x = 14 or x = 7 On subtracting (1) from (2), 2y = 10 or y = 5 Answer: Number = 7 + 10 x 5 = 57

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Answer 2

Hey !!

Answer:

Original Number

1st digit = x

2nd digit = 12 - x

According to place value , the number will be = 10x + 12 - x

                                                                                = 9x + 12

Interchanged number

1st digit = 12 - x

2nd digit = x

According to place value , the number will be = 10 ( 12 - x ) + x

                                                                                = 120 - 10x + x

                                                                                = 120 - 9x

Given , second number exceeds the first number by 18 ,

Equation

9x + 12  + 18 = 120 - 9x

9x + 30 = 120 - 9x

On transposing ,

9x + 9x = 120 - 30

18x = 90

x = 90/18

  = 5 .

Hence ,

Original  number = 57

Interchanged number = 75

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