Question

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

Whose income is highest ?

• A. A
• B. B
• C. C
• D. D

Answer 1

The correct option is B B

We have, $A+B>C+D...\left(1\right)$
$A+C=B+D...\left(2\right)$
$A=$ $\frac{1}{2}(B+D)...\left(3\right)$
Putting the value of $A$ in Eq. $\left(2\right),$ we get $C=\frac{1}{2}(B+D)$
i.e., $A=C$
Since, $A+B>C+D$ and $A=C$, we get $B>D$
Thus from eq. $\left(3\right),$ we get $B>A$ and $B>D$.
Clearly B has the highest score.
Hence, option 'B' is correct.