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.
Answers
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.
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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
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