Math, asked by tejalyadav22179, 11 months ago

A two digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or multiplying the difference of the digits by 16 and then adding 3.find the number.

Answers

Answered by Ritiksuglan
3

Answer:

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Solution :-

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) - 5

10x + y = 8x + 8y - 5

10x - 8x + y - 8y = - 5

2x - 7y = - 5  .................(1)

And,

10x + y = 16(x - y) + 3

10x + y = 16x - 16y + 3

10x - 16x + y + 16y = 3

- 6x + 17y = 3  ................(2)

Now, multiplying the equation (1) by 17 and (2) by 7, we get

34x - 119y = - 85 ...............(3)

- 42x + 119y = 21 ..............(4)

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

   34x - 119y = - 85

- 42x + 119y =   21

_________________

 - 8x             = - 64

_________________

⇒ 8x = 64

x = 64/8

x = 8 

So, tens digit is 8.  

Substituting the value of x = 8 in (1), we get

2x - 7y = - 5

2*8 - 7y = - 5

16 - 7y = - 5

- 7y = - 5 - 16

- 7y = - 21

7y = 21

y = 21/7

y = 3

Ones digit is 3.

So, the required number is 83.

Answer.

May be it's helpful for you

Answered by surendarrajawat
1

Hey MATE!

Let the number at tens place is x and the number at unit place is y.

Therefore the 2 digit number is (10x+y).

The equations we get from above conditions are :

8(x+y) -5 = 10x +y --- equation 1.

16(x-y) + 3 = 10x +y ------ equation 2.

Solving the equation we get

X = 8 and Y = 3 Answer.

Hence the digit is 83.

Hope it helps

HAKUNA MATATA :))

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