# The digits of both the two-digit numbers in the first calculation below have been reversed to give the two-digit numbers in the second calculation

Question: The digits of both the two-digit numbers in the first calculation below have been reversed to give the two-digit numbers in the second calculation. The answers to the two calculations are the same. 62 × 13 = 806 26 × 31 = 806 For which one of the calculations below is the same thing true?

ab  * cd
= (10a + b) * (10c + d)
= 100ac  + 10(ad + bc)  +  bd
ba * cd

= (10b + a)(10d + c)
= 100bd  + 10(ad + bc)  + ac

Sync both
100ac  + 10(ad + bc)  +  bd  = 100bd  + 10(ad + bc)  + ac
=> 99ac  =  99bd
=> ac = bd

It will be right for the numbers that will satisfy this

Like here  a = 2   b = 6      c  = 3   d = 1
ac = bd = 6

So we can take example like this
43    &   68     or      46     &   32

As options below are not given so Correct option can be find out
bu Simply checking if a*c = b*d    ( for number ab & cd)

42  * 48  = 24 * 84