A) \[{{p}_{B}}+{{x}_{A}}({{p}_{B}}-{{p}_{A}})\]
B) \[{{p}_{A}}+{{x}_{A}}({{p}_{A}}-{{p}_{B}})\]
C) \[{{p}_{A}}+{{x}_{A}}({{p}_{B}}-{{p}_{A}})\]
D) \[{{p}_{B}}+{{x}_{A}}({{p}_{A}}-{{p}_{B}})\]
Correct Answer: D
Solution :
\[{{P}_{M}}=P{{'}_{A}}+P{{'}_{B}}\] \[={{P}_{A}}.{{x}_{A}}+{{P}_{B}}.{{x}_{B}}(\because \,P{{'}_{A}}={{P}_{A}}.{{x}_{A}})\] \[={{P}_{A}}.{{x}_{A}}+{{P}_{B}}(1-{{x}_{A}})(\because \,{{x}_{A}}+{{x}_{B}}=1)\] \[={{P}_{B}}+{{x}_{A}}+({{P}_{A}}-{{P}_{B}})\]You need to login to perform this action.
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