**Solution:**

Let *a*_{1}, *a*_{2}, and *d*_{1}, *d*_{2} be the first terms and the common difference of the first and second arithmetic progression respectively.

According to the given condition,

Substituting *n* = 35 in (1), we obtain

From (2) and (3), we obtain

**Thus, the ratio of 18th term of both the A.P.s is 179: 321.**