A man buys a house for ₹5 lakh and rents it. He puts $12 \frac{1}{2} \%$ of each month's rent aside for repairs, pays ₹1660 as annual taxes and realizes 10\% on his investment thereafter. Find the monthly rent of the house. (M.A.T., 2009)
Answer
Answer (as printed):
Explanation
Let the annual rent of the house be ₹$x$. Then, $$\begin{aligned} & x-\left(12 \frac{1}{2} \% \text { of } x+1660\right)=10 \% \text { of } 500000 \\ & \Rightarrow x-\left(\frac{25}{2} \times \frac{1}{100} \times x+1660\right)=50000 \\ & \Rightarrow \frac{7 x}{8}-1660=50000 \Rightarrow \frac{7 x}{8}=51660 \Rightarrow x=\left(\frac{51660 \times 8}{7}\right)=59040 . \\ & \text { Hence, monthly rent }=₹\left(\frac{59040}{12}\right)=₹ 4920 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.