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.

If A's income be Rs. $80,000$ per annum and the difference between the income of B and D be the same as A's income, B's income is

• A. Rs. $40,000$
• B. Rs. $60,000$
• C. Rs. $80,000$
• D. Rs. $1,20,000$

Answer 1

The correct option is D Rs. $1,20,000$

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. (2), 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 $B>C$.
$2A=B+D...\left(1\right)$
$A=B-D...\left(2\right)$
Adding eq. (1) and (2), we get
$3A=2B$
$A=80,000\left(given\right)$
$\therefore B=\frac{3}{2}\times 80000$
$B=Rs1,20,000$
Hence, option 'D' is correct.