If on dividing 26 into two parts, we find that three times the first and seven times the second part together equals to 122. Then, the ratio of first and second part shall be:

15:11

The correct answer is Option (1) → 15:11

Let the two parts be $x$ and $26 - x$.

According to the condition:

$3x + 7(26 - x) = 122$

$3x + 182 - 7x = 122$

$-4x = 122 - 182 = -60$

$x = 15$

Second part = $26 - 15 = 11$

Required ratio = $\frac{15}{11}$