The electron gain enthalpy values of four successive elements A, B, C and D of 3rd period are respectively –135, –60, –200 and –348kJ/mole. The outer electronic configuration of element 'B; is

Electron gain enthalpy values of P(-60KJ)<Si(-135KJ)<S(-200KJ)<Cl(-348KJ). 15th group elements due to stable configuration will have lesser electron gain enthalpy value as compared to the preceding 14th group element 
∴ A is 'Si',B is 'P',C is 'S',D is 'Cl';

Let us try trial and error method in 3rd period;

Suppose if A is Na, then B must be Mg which has positive EGE;

So we cannot start with Na or even with Mg;

Suppose if we start with Al then B will be Si but EGE of Si is more than that of Al ; In the given data, EGE of B is less than A;

So we cannot start with Al ;

So if we start with silicon the given data will match;