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.

Which of the following statements is not correct ?

• A. A earns more than B
• B. B earns more than D
• C. C earns more than D
• D. B earns more than C

Answer 1

The correct option is A A earns more than 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. (iii), we get $B>A$ and $B>C$.
Clearly, B earns more than A and hence, the statement in A is false.
Hence, option 'A' is correct.