Question

A two digit number is 7 times the sum of its digits if the difference between two digit is 2 find the number

Answer 1

Hey
Here's your answer !!
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Let the unit's digit be x .
There fore , ten's digit will be ( x + 2 ) .
There fore , the number is 10 ( x + 2 ) + x
= 10 x + 20 + x
= 11 x + 20 .

According to the question ,

11 x + 20 = 7 ( x + x + 2 )
=> 11 x + 20 = 14 x + 14
=> 3 x = 6
=> x = 2 .

There fore , units digit = 2 .
So , tens digit = 4 .

So the number is 42.
But it can also be the other way round , that is , units digit be 4 and tens digit be 2 .
In that case, the number will be 24 .
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Hope it helps !!

Answer 2

HI !

Let the digit in unit's place be "y" and the digit in ten's place be "x"

Then the two digit no: is 10x + y

A.T.Q.,

7(x + y) = 10x +  y

7x + 7y =  10x + y 

3x - 6y = 0

3( x- 2y) = 0

x - 2y = 0               ---> (1)

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also,

x - y = 2          --->(2)

(1) - (2)

x - 2y = 0
x - y = 2
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-y = -2

y = 2

x  - 2y = 0
x - 4 = 0

x = 4

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The no: is -->

10x + y --->  10(4) + 2 = 42

42 is the no: