hi aatish

see since total k.e remains same

therefore P1V1=P2V2  (bcoz  total k.e = 3/2PV)

also since molecules are inside the box therefore volume occupied is same hence V remains constant

now from ideal gas equations

P1V = nRT1

P2V = 2nRT2  (since molecules are doubled therefore no. of moles is doubled)   

& P1V = P2V   (reason as mentioned in 2nd & 3rd line)

From the above equations P1 = P2 & T2 = T1/2