2026/026) The number of solution-pairs in the positive integers of the equation 3x+5y=501 is:(A) 33(B) 34(C) 35(D) 100(E) none

We have 501 = 495 (multiple of 15) + 6

6 = 3 * 2

So 501 = 2 * 3 + 99 * 5

As 3 * 5 = 5 * 3

We have 501 = 3 (2 + 5t) + 5 ( 99 - 3t)

If t is zero or positive coefficient of 3 is positive and t -ve coefficient of 3 is -ve . We need to ensure 99 - 3t positive so t is less than 33 so 33 values 0 to 32

Hence answer (A) 33