Question

Two yrs ago, Sam was two-thirds of Pam's age ( at that time). In three years, Same will be three-fourths of Pam's age. In 20 yrs, the sum of their ages will be 61. How old is Sam?

Answer 1

3(s-2) = 2(p-2)
4(s+3) = 3(p+3)
s = 12, p=17
two years ago, 10 = 2/3 (15) ✔
in three years, 15 = 3/4 (20) ✔
But in 20 years, 32+37 = 69

Answer 2

Your question is gobble-de-goop

You have 3 conditions imposed on two unknowns, which in this case
leads to a contradiction, as shown when the previous tutor shows that the
solution based on the first two conditions does not satisfy the third condition.

Suppose I solve it based only on the last two conditons:
Let Sam's present age be s, and Pam's current age be p

3 years from now,
Sam will be s+3, and Pam will be p+3
At that time, Sam's age will be three-fourths of Pam's age
---> s+3 = (3/4)(p+3)
4s + 12 = 3p + 9
4s - 3p = -3

third condition: in 20 years, the sum of their ages will be 61
---> s+20 + p+20 = 61
s+p = 21 or p = 21-s
sub into 4s - 3s = -3
4s - 3(21-s) = -3
7s = 60
s = 8.57 , let's say 8 1/2, then Pam is 21-s = appr 12 1/2

different answers, both satisfy your 2nd and your 3rd condition, but not the first.

Check your question!