Correct Answer - Option 3 : 6, 4
By checking the following alternatives.
1) X = 3, Y= 4
Given: 39x52 + 278y = y2y3x
39352 + 2784 = 42433
4213 ≠ 42433
2) X = 4, Y = 2
Given: 39x52 + 278y = y2y3x
39452 + 2782 = 22234
42234 ≠ 22234
3) X= 6, Y= 4
Given: 39x52 + 278y = y2y3x
39652 + 2784 = 42436
424367 = 42436
4) X = 6, Y = 3
Given: 39x52 + 278y = y2y3x
39652 + 2783 = 32336
42435 ≠ 32336
Hence, '6, 4' is the correct answer.