A) \[\frac{S+T}{2}\]
B) \[\frac{S+11T}{2}\]
C) \[\frac{1}{11S}+T\]
D) \[\frac{11S+T}{12}\]
Correct Answer: D
Solution :
Let the number of agricultural and other workers be \[{{n}_{1}}\] and \[{{n}_{2}}\] \[\therefore \] \[{{n}_{1}}=11\,{{n}_{2}}\] ...(i) Sum of monthly income of agricultural workers =\[=s\,{{n}_{1}}\] Sum of monthly income of other workers \[=T\,{{n}_{2}}\] Sum of monthly income of all workers \[=S\,{{n}_{1}}+T\,{{n}_{2}}\] \[\therefore \] Average monthly income of all workers \[=\frac{S{{n}_{1}}+T{{n}_{2}}}{{{n}_{1}}+{{n}_{2}}}=\frac{S(11{{n}_{2}})+T{{n}_{2}}}{11{{n}_{2}}+{{n}_{2}}}\] \[=\frac{{{n}_{2}}(11S+T)}{{{n}_{2}}(11+1)}=\frac{11S+T}{12}\]
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