Question

. A two digit number is obtained by either multiply the sum of the digits by 8 and adding 1 or by
multiplying the difference of the digits by 13 and adding 2. Find the number

Answer 1

Answer:

let the two digit number be 10x+y.,  

then, according to question,

10x + y =  (x + y)

8+1 => 2x - 7y = 1 ..... (1)  

also,

10x + y

= (x - y) 13 + 2

=> -3x + 14 y = 2 ...... (2)

Multiplying equation (1) by 2 and adding euation (2), we get

(4x - 14y) + (-3x +1 4y) = 2 + 2

=> x=4

Substituting this value of x in equation (1),we get

40 + 4 = 32 + 8y + 1

=> y = 1

Hence, the number is 41

Answer 2

ANSWER:

As, it is mentioned the number is a two digit number so,

let the number in tens place be x

and

let the number in digits place be y.

Number: 10x+y

Also given in the question in the first part; the two digit number is obtained by either multiply the sum of the digits by 8 and adding 1

So,

10x+y= 8(x+y)+1

10x+y= 8x+8y+1

10x-8x-8y-y=1

2x-7y=1

Let's mark 2x-7y=1 as equation. 1

Now,solving the second part, multiplying the difference of the digits by 13 and adding 2.

10x+y= 13(x+y)+2

10x+y=13x+13y+2

10x-13x+13y+y=2

-3x+14y=2

Let's mark -3x+14y=2 as equation 2

Now, multiply equation 1 by 2 and add in equation. 2

2x-7y =1=>1(multiply by 2)

4x-14y=2

Let's mark 2

4x-14y=2 as equation. 3

Now add equation 2 and 3,

-3x+14y=2

+ 4x-14y =2

____________

x =4

Now put x=4 in equation 1

2(4)-7y =1

8 -7y =1

8 -1 =7y

7y = 7

y =7/7

y =1

So, now look out for the values of x and y,

x=4

and

y=1

So, the number therefore=41