Question

3. When a two digit number is reversed it gets
decreased by 72, what is the number?
(a) 81
(b) 72
(c) 91
(d) 64​

Answer 1

Answer:

The correct option will be - (c) 91

Step-by-step explanation:

Say the digit in one's place is  '' y ''

and the digit in Ten's place is  '' x ''

so the number will be  10*x + y

Now if we reverse it then it gets decreased by 72

so by reversing the digits the '' x '' will be placed in one's position

and the '' y '' will be placed in Ten's position.

So the Reversed number will be 10*y + x

According to our problem condition we can write

(10*x + y) - 72 = (10*y + x)

or 10x + y - 72 - 10y - x = 0

or 9x - 9y - 72 = 0

or 9*( x - y - 8 ) = 0

or x - y - 8 = 0

or x = y + 8

Now

from the given options

if we take option (c) the actual number will be 91

so respect to our assumption x = 9 and y = 1

now we need to check the equation if its gets satisfied or not

x = 9

and y + 8 = 1 + 8 = 9

so our chosen answer is correct.

Answer 2

Answer:

When a two digit number =91 is reversed it gets

decreased by 72.

Step-by-step explanation:

lets take the first and second digit be a and y.

So the Reversed number will be 10*y + a

Say the digit in one's place is  '' y ''

and the digit in Ten's place is  '' a ''

so the number will be  10*a + y

Now if we reverse it then it gets decreased by 72

so by reversing the digits the '' a '' will be placed in one's position

and the '' y '' will be placed in Ten's position.

According to our problem condition we can write

(10*a + y) - 72 = (10*y + a)

or 10a + y - 72 - 10y - a = 0

or 9a - 9y - 72 = 0

or 9*( a - y - 8 ) = 0

or a - y - 8 = 0

or  = y + 8

Now

from the given options

if we take option (c) the actual number will be 91

so respect to our assumption a = 9 and y = 1

now we need to check the equation if its gets satisfied or not

a = 9

and y + 8 = 1 + 8 = 9

so our chosen answer is correct.

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