1. **State the problem:** We are given the sum of the first 10 terms of an arithmetic progression (A.P.) as 240 and the 8th term as 34. We need to find the common difference $d$ of the A.P. 2. **Recall relevant formulas:** - Sum of first $n$ terms: $S_n = \frac{n}{2}(2a + (n-1)d)$ where $a$ is the first term and $d$ the common difference. - The $n$th term formula: $a_n = a + (n-1)d$ 3. **Given:** - $S_{10} = 240$ - $a_8 = 34$ 4. **Write the equations using the given data:** From sum formula for $n=10$: $$ S_{10} = 5(2a + 9d) = 240 \implies 2a + 9d = 48 \quad \text{(equation 1)} $$ From $8$th term formula: $$ a + 7d = 34 \quad \text{(equation 2)} $$ 5. **Express $a$ from equation (2):** $$ a = 34 - 7d $$ 6. **Substitute $a$ into equation (1):** $$ 2(34 - 7d) + 9d = 48 $$ Simplify: $$ 68 - 14d + 9d = 48 $$ $$ 68 - 5d = 48 $$ 7. **Solve for $d$:** $$ -5d = 48 - 68 = -20 $$ $$ d = \frac{-20}{-5} = 4 $$ **Final answer:** The common difference is $\boxed{4}$.