Question

a number consists of two digit when the number is divided by the sum of its digit the quotient is 7 if 27 is subtracted from the no the digit interchange their places find the numbers​

Answer 1

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Answer 2

Given:-

• A number consists of two digits when the number is divided by the sum of digit the quotient is 7.
• If 27 is subtracted from the numbers, the digits interchange their places.

To find:-

• Find the number ?

Solutions:-

• Let the digit at unit's place be 'y' and the digit at ten's place be 'x'

Then,

Number = 10x + y

A number consists of two digits when the number is divided by the sum of digit the quotient is 7

According to the questions:-

=> (10x + y)/(x + y) = 7

Use cross multiplication

=> 10x + y = 7(x + y)

=> 10x + y = 7x + 7y

=> 10x - 7x = 7y - y

=> 3x = 6y

=> x = 2y ......(i).

If 27 is subtracted from the numbers, the digits interchange their places.

Number obtained by reversing the digits = 10y + x

Original number - 27 = Number obtained by reversing the digits

According to the questions:-

=> 10x + y + 27 = 10y + x

=> 10x - x + y - 10y = -27

=> 9x - 9y = -27

=> 9(x - y) = -27

=> x - y = -27/9

=> x - y = -3 ......(ii).

Putting the value of 'x' from equation (i) in equation (ii)

=> x - y = -3

=> 2y - y = -3

=> y = -3

Now, put the value of 'y' in equation (i)

=> x = 2y

=> x = 2(-3)

=> x = -6

Now,

Number = 10x + y

=> 10(6) + 3

=> 60 + 3

=> 63

Hence, the number is 63.