Question

$A$ owes $B$ Rs. $1573$ payable $1\frac{1}{2}$ years hence. Also $B$ woes $A$ Rs. $1444$. $50$ payable $6$ months hence. If they as the rate of interest, then who should pay whom and how much?

• A. $A$ to $B$ Rs. $28.50$
• B. $B$ to $A$ Rs. $37.50$
• C. $A$ to $B$ Rs. $50$
• D. $B$ to $A$, Rs. $50$

Answer 1

Answer: (D)

$B$ to $A$, Rs. $50$

Let the present value of what $A$ owes $B$ be Rs. $x$.
Then, $x+$ $\frac{x\times 14\times 3}{2\times 100}=1573$
$\Rightarrow x+\frac{21x}{100}=1573$

$\Rightarrow \frac{121x}{100}=1573$
$\Rightarrow x=\frac{1573\times 100}{121}=1300$
Let $y$ be the present value of what $B$ owes $A$.
Then, $y+y\times$ $\frac{1}{2}\times \frac{14}{100}=1444.50$
$\Rightarrow y+\frac{7y}{100}=1444.50$

$\Rightarrow 107y=1444.50\times 100$
$\Rightarrow y=\frac{144450}{107}=Rs1350$
Hence, $B$ must pay Rs. $50$ to $A$.