Ping issue: connect a switch into another switch's vlan port

Question

I have a Cisco 2960-X switch and a Cisco SG-300 switch. I created VLANs on 2960-X switch (e.g. VLAN 10 with ports 1-5 and VLAN 20 with ports 6-10) and allow DHCP for each VLAN.

Now, laptop 10.10.1.2 and laptop 10.10.2.2 can ping each other successfully.

After this:

1. I connect SG-300 into a port of VLAN 20. VLAN 20 assigns it an IP address 10.10.2.3 by DHCP.
2. I connect a third laptop into one port of SG-300 switch. It got an IP address 10.10.2.4 automatically (I did not do any configure on SG-300, a new switch)
3. laptop 10.10.2.4 can ping 10.10.1.2 successfully.
4. laptop 10.10.1.2 can ping 10.10.2.3, but cannot ping 10.10.2.4, which is behind SG-300 switch.

Hence, to make 10.10.1.2 ping 10.10.2.4 each other successfully, how to configure SG-300 switch?

Answer 1

(copying from the comments as it was confirmed to be the solution)

If 10.10.2.4 can ping 10.10.1.2 successfully then L2 and L3 connectivity appear to be ok and so 10.10.1.2 should also be able to ping 10.10.2.4. If not, then the most likely explanation is that a host-based firewall on 10.10.2.4 is dropping the pings.

Answer 2

To ensure communication between IP address 10.10.1.2 and 10.10.2.4 both ip address belongs to different Vlans to ensure communication between different Vlans inter-Vlan need to be done , for doing inter-Vlan routing layer3 device is required . Where as cisco 2960 is layer2 device . Move both Vlans to Cisco SG300 switch hence this switch has layer3 capabilities inter-Vlan routing can be done in sg300 switch .. further connect Cisco 2960 switch trunk link allowing both Vlans passing through this link connecting access-list and SG300 switch .