The sum of the incomes of A and B is more tha | vedclass

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Question

(B) Given conditions:$A + B > C + D$ ... $(1)$$A + C = B + D$ ... $(2)$$A = \frac{1}{2}(B + D)$ ... $(3)$From equation $(2)$,we have $C = (B + D) - A$

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$B$

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(B) Given conditions:$A + B > C + D$ ... $(1)$$A + C = B + D$ ... $(2)$$A = \frac{1}{2}(B + D)$ ... $(3)$From equation $(2)$,we have $C = (B + D) - A$. Substituting the value of $A$ from equation $(3)$:$C = (B + D) - \frac{1}{2}(B + D) = \frac{1}{2}(B + D)$.Thus,$A = C$.Now,substitute $A = C$ into equation $(1)$:$A + B > A + D$,which simplifies to $B > D$.From equation $(3)$,since $A = \frac{1}{2}(B + D)$ and $B > D$,it follows that $A$ is the average of $B$ and $D$. Since $B$ is greater than $D$,$B$ must be greater than the average $A$ (i.e.,$B > A$).Since $A = C$ and $B > A$,it follows that $B > C$ as well.Therefore,$B$ has the highest income.

The sum of the incomes of $A$ and $B$ is more than that of $C$ and $D$ taken together. The sum of incomes of $A$ and $C$ is the same as that of $B$ and $D$ taken together. Moreover,$A$ earns half as much as the sum of the incomes of $B$ and $D$. Whose income is the highest?

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