Q155
ReasoningSeating Arrangement, Ranking & Puzzles
The sum of the incomes of A and B is more than that of C and D taken together. The sum of the 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?
- a.A
- b.B
- c.C
- d.D
Answer: (B) B
Let $A+C = B+D = k$. Since $A = \dfrac{1}{2}(B+D) = \dfrac{k}{2}$, we get $C = k - A = \dfrac{k}{2}$, so $A=C=\dfrac{k}{2}$. Also, since $A+B>C+D$ and $A=C$, it follows that $B>D$. Since $B+D=k$ and $B>D$, we must have $B>\dfrac{k}{2}$, so $D<\dfrac{k}{2}$. Putting it together: $D < A = C < B$, so B's income is the highest.