Question

A 2digit number is obtained by either multiplying the sum of its digit by 8 and by adding 1 or multiplying the difference of digit by 13 and adding 2,find the number

Answer 1

Let the digit at ten's and one's place be x and y respectively.

so, 8(x+y)+1=10x+y
and
13(x-y)+2=10x+y

solving these two equations we get
x=4, y=1
so the required number is 41

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Correct Question - Two digit number is obtained by either multiplying the sum of the digits by 8 and adding one or 5 multiplying the difference of digits by 13 and then adding 2 then find the number.

Solution :-

Assumption

Tens digit be p

Unit digit be t

Number = 10p + t

Situation,

10p + t = 8(p + t) + 1

10p + t = 8p + 8t + 1

2p - 7t = 1 .......................... (1)

10p + t = 13(p - t) + 2

10p + t = 13p - 13t + 2

-3p + 14t = 2 ...................... (2)

Now,

Multiply (1) by -3 and (2) by 2,

-7t = 7

t = 7/7

t = 1

Now,

Substitute the value of t in (1)

2p - 7t = 1

2p - 7(1) = 1

2p - 7 = 1

2p = 1 + 7

2p = 8

p = 8/2

p = 4

Hence,

Number = 10p + t

= 10(4) + 1

= 40 + 1

= 41