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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Solve the following pair of linear equation by cross - multiplication method:

x + 4y + 9 = 0

5x – 1 = 3y

KC Sinha - MathematicsSolve each of the following systems of equations by using the method of cross multiplication:

2x + y = 35, 3x + 4y = 65.

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