Q. 205.0( 5 Votes )
A number consists of two digits. When it is divided by the sum of its digits, the quotient is 6 with no remainder. When the number is diminished by 9, the digits are reversed. Find the number.
Answer :
Let unit’s digit = y
and the ten’s digit = x
So, the original number = 10x + y
The sum of the number = 10x + y
The sum of the digit = x + y
According to the question,
⇒ 10x + y = 6(x + y)
⇒ 10x + y = 6x + 6y
⇒ 10x + y – 6x – 6y
⇒ 4x – 5y = 0 …(i)
The reverse of the number = x + 10y
and 10x + y – 9 = x + 10y
⇒ 10x + y – 9 = x + 10y
⇒ 10x – x + y – 10y = 9
⇒ 9x – 9y = 9
⇒ x – y = 1
⇒ x = y + 1 …(ii)
On substituting the value of x = y + 1 in Eq. (i), we get
4x – 5y = 0
⇒ 4(y + 1) – 5y = 0
⇒ 4y + 4 – 5y = 0
⇒ 4 – y = 0
⇒ y = 4
On substituting the value of y = 4 in Eq. (ii), we get
x = y + 1
⇒ x = 4 + 1
⇒ x = 5
So, the Original number = 10x + y
= 10×5 + 4
= 50 + 4
= 54
Hence, the two digit number is 54.
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