Question

¿¿¿a two digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3 find the number???
[give clear answer with solution]
====>answer is 83 <======

Answer 1

let the two digit number be "10a+b"
Now according to the question.

condition 1
10a+b=8(a+b)-5 which gives
2a-7b= -5  ...............(i)

condition 2
10a+b=16(a-b)+3 which gives
-6a+17b=3  ..........(ii)

performing (i)x3 + (ii) we get

17b-21b=3-15
4b=12
b=3

substituting the value of b in equation (i) we get
a=[-5+(7x3)]/2
a=8

So the original number is 10a+b
=10x8+3
=83

Answer 2

$<b><u><i>$Refer to the attachment

$<b><u><i>$Solving the both equations we will get the values of a = 8 , b = 3