Two solids dissociate as follows

$A(s)\, \rightleftharpoons \,B(g)\, + \,C(g)\,\,;\,\,\,{K_{P1}}\, = \,x\,at{m^2}$
$D(s)\, \rightleftharpoons \,C(g)\, + \,E(g)\,\,;\,\,\,{K_{P2}} = \,y\,at{m^2}$

The total pressure when both the solids dissociate simultaneously is

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answer is C.

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Detailed Solution

When both the solids dissociate simultaneously

$\large A\left( s \right) \rightleftharpoons \mathop {B\left( g \right)}\limits_{{P_1}} + \mathop {C\left( g \right);}\limits_{{P_1} + {P_2}} {K_{{P_1}}} = xatm = {P_1}\left( {{P_1} + {P_2}} \right) \to \left( 1 \right)$

$\large D\left( s \right) \rightleftharpoons \mathop {C\left( g \right)}\limits_{{P_1} + {P_2}} + \mathop {E\left( g \right);}\limits_{{P_2}} {K_{{P_2}}} = yatm = {P_2}\left( {{P_1} + {P_2}} \right) \to \left( 2 \right)$

$\large {P_T} = {P_1} + \left( {{P_1} + {P_2}} \right) + {P_2} = 2\left( {{P_1} + {P_2}} \right) \to \left( 3 \right)$

$\large \left( 1 \right) + \left( 2 \right) \Rightarrow {K_{{P_1}}} + {K_{{P_2}}} = {\left( {{P_1} + {P_2}} \right)^2} \Rightarrow {P_1} + {P_2} = \sqrt {{K_{{P_1}}} + {K_{{P_2}}}}$