Question

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?

• A. $A$
• B. $B$
• C. $C$
• D. $D$

Answer 1

Answer: (B)

$B$

Given :

$A+B>C+D$ ........ (1)

$A+C=B+D$ ........ (2)

$A=\frac{B+D}{2}$, so from (2) we get $C=\frac{B+D}{2}=A$

Substituting $A$ and $C$ in (1) we get,

$B>D$

From (1) and (2), we conclude that $C<B$

So, $B>C=A$ and $B>D$.

Hence, $B^{\prime }s$ income is the highest.