Explanation:

Let the number of stones at each side of the middle stone be n (i.e., total of 2n+1 stones)
(Let M be the middle stone, A1...An be the stones at the left, B1...Bn be the stones at the right)
Consider he picks the stone B1 and brings it back to the middle. Distance travelled = 2 × 10
Then he picks the stone B2 and brings it back to the middle. Distance travelled = 2 × 2 × 10
For B3, distance travelled =2 × 3 × 10.
For Bn, distance travelled = 2×n×10
Total distance travelled for bringing back all the stones at the right
= 2 × 10 +  2 × 2 × 10 + 2 × 3 × 10 + ... + 2 × n × 10
= 2 × 10 [1 + 2 + ... + n] 
Then he picks A1 and returns. Same pattern is continued. Distance travelled to bring back all the stones at left will be same as 2 × 10 [1 + 2 + ... + n]
Total distance travelled = 2 × 2 × 10 [1 + 2 + ... + n]
= 2 × 2 × 10 [1 + 2 + ... + n] = 4800
= [1 + 2 + ... + n]  = 120
= n(n+1)2n(n+1)2 = 120
= n(n+1) = 240
= n2 + n - 240 = 0
= (n + 16)(n - 15) = 0
= n = 15 (ignoring the negative value)
Number of stones = 2n+1 = 2×15+1 = 31

Hence, option 4 is the correct answer.