Question

The sum of the digits of a two digit number is 7. If 27 is subtracted from it, the digits are reversed. Find the product of the digit.​

Answer 1

Answer:

10

Step-by-step explanation:

Concept= Algebra of numbers

Given= Sum of 2 digit number and difference of their reverse

To Find= The product of two digit number

Explanation=

We have been provided with the information that

The sum of the digits of a two digit number is 7.

If 27 is subtracted from it, the digits are reversed.

So according to this we now a two digit comprises of unit place and ten's place. The number is also in the form of 10a + b, where a=ten's place digit and b= unit place digit.

Let us take the ten's place digit be x and unit be y.

Two Digit number will be 10x + y.

The sum of x and y is 7.

x + y=7, x= 7-y

Reverse of this two digit number will be 10y + x.

So, 10y + x = 10x + y -27

9x - 9y = 27

x - y = 3

substitute x= 7-y in x-y=3 we get,

7 - y-y = 3

2y= 4

y= 2.

x= 5.

Therefore the two digit number 10x+y = 10*5 + 2= 52.

The product of 52= 5*2= 10

Therefore the product of the two digit number is 10.

#SPJ2

Answer 2

Answer:

The product of the digits = 10

Step-by-step explanation:

Given,

The sum of digits of a number = 7

When 27 is subtracted from it, the digits are reversed

To find,

The product of the digits

Solution

Let the number be 10x+y

The digits are x,y

Since the sum of digits = 7, we have

x+y = 7 --------------------(1)

The number reversed by reversing the digits = 10y+x

Since 27 is subtracted from it, the digits are reversed, we get

10x+y -27 = 10y+x

x - y = 3 -------------------(2)

Adding equations(1) and (2) we get

2x = 10

x = 5

Substitute the value of 'x' in equation(1) we get

5+y = 7

y = 2

The digits of the number are = 5,2

The product of the digits = 10

#SPJ2