Q. 223.9( 7 Votes )
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. The number is
A. 96
B. 69
C. 87
D. 78
Answer :
Let us assume the tens and the unit digits of the required number be x and y respectively
∴ Required number = (10x + y)
According to the given condition in the question, we have
x + y = 15 (i)
By reversing the digits, we obtain the number = (10y + x)
∴ (10y + x) = (10x + y) + 9
10y + x – 10x – y = 9
9y – 9x = 9
y – x = 1 (ii)
Now, on adding (i) and (ii) we get:
2y = 16
Putting the value of y in (i), we get:
x + 8 = 15
x = 15 – 8
x = 7
∴ Required number = (10x + y)
= 10 × 7 + 8
= 70 + 8
= 78
Hence, option D is correct
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