Question

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A two digit number is obtained by multiplying the sum of the digits by 8.
Also , it is obtained by multiplying the difference of the digits by 14 and adding 2.
Find the number.......




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THOSE WHO KNOW THE ANSWER CAN ANSWER......✔✔✔​

Answer 1

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Let the two digit number be 10x + y where x is the tens digit and y is the ones digit.

Now, according to the question.

10x + y = 8(x + y)

10x + y = 8x + 8y

10x - 8x + y - 8y =0

2x - 7y = 0 .................(1)

And,

10x + y = 14(x - y) + 2

10x + y = 14x - 14y + 2

10x - 14x + y + 14y = 2

- 4x + 15y = 2 ................(2)

Now, multiplying the equation (1) by 4 and (2) by 2, we get

8x - 28y =0 ...............(3)

- 8x + 30y =8 ..............(4)

Now, adding (3) and (4), we get

8x - 28y = 0

- 8x + 30y = 8

_________________

2y = 8

_________________

⇒ 2y = 8

y = 8/2

y = 4

So, ones digit is 4.

Substituting the value of y=2 in (1), we get

2x - 7y = 0

2x - 7*(2) = 0

2x -14 = 0

2x=0 +14

2x= 14

X=14/2

X=7

tens digit is 7 .

So, the required number is 74

Answer 2

let the number be

z

and other two digit be x and y

according to question

8(x + y)= 10x + y

- 2x = -7y

x = 7y/2

again

14(x - y)+2 = 10x + y

14( 5y)/2 + 2 = 36y

y = 2

so

x = 7

number = 10*7+2=72