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
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
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(a) 96
Let the tens and the units digits of the required number be x and y, respectively.
Required number = (10x + y)
According to the question, we have:
x + y = 15 ……..(i)
Number obtained on reversing its digits = (10y + x)
∴ (10y + x) = (10x + y) + 9
⇒ 10y + x – 10x – y = 9
⇒ 9y – 9x = 9
⇒ y – x = 1 …….(ii)
On adding (i) and (ii), we get:
2y = 16
⇒ y = 8
On substituting y = 8 in (i), we get:
x + 8 = 15
⇒ x = (15 – 8) = 7
Number = (10x + y) = 10 × 7 + 8 = 70 + 8 = 78
Hence, the required number is 78.
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