Raj and Vikram are two travelers in ancient India, walking along the Silk road. On the first day of travel, Raj travels 5 yojanas, and on each successive day travels 3 yojanas more than the previous day. Vikram started at the same place and travels the same path, but started 5 days earlier, and travels 7 yojanas a day. On which day of Raj's travel will the two of them meet?

To find out on which day Raj and Vikram will meet, we need to determine the total distance covered by each traveler until they meet.

Let's start by finding the total distance covered by Raj. On the first day, Raj travels 5 yojanas, and on each successive day, he travels 3 yojanas more than the previous day. So, for each day, we can represent the distance traveled by Raj as follows:

Day 1: 5 yojanas
Day 2: 5 + 3 = 8 yojanas
Day 3: 8 + 3 = 11 yojanas
Day 4: 11 + 3 = 14 yojanas

And so on...

So, we can create a sequence to represent the distance traveled by Raj:

5, 8, 11, 14, ...

Now, let's find the total distance covered by Vikram. Vikram started 5 days earlier than Raj and travels 7 yojanas per day. So, we can represent the distance traveled by Vikram on each day as follows:

Day 1: 0 (since Vikram started 5 days earlier)
Day 2: 7 yojanas
Day 3: 7 + 7 = 14 yojanas
Day 4: 14 + 7 = 21 yojanas

And so on...

So, we can create a sequence to represent the distance traveled by Vikram:

0, 7, 14, 21, ...

To find the day when Raj and Vikram meet, we need to find the common term in these two sequences.

One way to find the common term is by comparing the terms of the sequences. Notice that the terms of the first sequence are 5, 8, 11, 14, ... and the terms of the second sequence are 0, 7, 14, 21, ... Looking at the terms, we can see that the terms of the second sequence are always 7 less than the terms of the first sequence.

Since Vikram started 5 days earlier, we need to adjust the sequences accordingly. So, we need to shift the second sequence by 5 terms. Now, the second sequence becomes:

7, 14, 21, 28, ...

Now, we can compare the terms of the two sequences:

5, 8, 11, 14...
7, 14, 21, 28...

From the comparison, we can see that the common term in both sequences is 14. Therefore, Raj and Vikram will meet on the 4th day of Raj's travel.

So, the answer is that Raj and Vikram will meet on the 4th day of Raj's travel.