The sum of the digits of a two-digit number is 15. The number obtained

1.	The sum of the digits of a two-digit number is 15. The number obtained by interchanging the digits exceeds the given number by 9. Find the number.
Answer» Let us consider, one’s digit of a two digit number = x and ten’s digit = y The number is x + 10y After interchanging the digits, One’s digit = y and ten’s digit = x The number is y + 10x As per the statement, x + y= 15 ………….(1) And, y + 10x = x + 10y + 9 y + 10x – x – 10y = 9 9x – 9y = 9 x – y = 1 …(2) On adding, we get 2x = 16 Or x = 8 On subtracting (2) from (1) 2y = 14 y = 7 Answer: Number = x + 10y = 8 + 10( 7) = 78

The sum of the digits of a two-digit number is 15. The number obtained by interchanging the digits exceeds the given number by 9. Find the number.

Answer»

Let us consider, one’s digit of a two digit number = x and

ten’s digit = y

The number is x + 10y

After interchanging the digits,

One’s digit = y and

ten’s digit = x

The number is y + 10x

As per the statement,

x + y= 15 ………….(1)

And,

y + 10x = x + 10y + 9

y + 10x – x – 10y = 9

9x – 9y = 9

x – y = 1 …(2)

On adding, we get

2x = 16

Or x = 8

On subtracting (2) from (1)

2y = 14

y = 7

Answer:

Number = x + 10y = 8 + 10( 7) = 78