A salesman's commission is 5\% on all sales up to ₹ 10000 and 4\% of all sales exceeding this amount. He remits ₹ 31100 to the parent company after deducting his commission. His sales were worth
(a)₹ 32500
(b)₹ 35000
(c)₹ 35100
(d)₹ 36100
Answer
Answer (as printed): A
Explanation
Let his total sales be ₹ $x$. Now, Total sales - Commission = ₹ 31100. $$\begin{aligned} \therefore x & -[5 \% \text { of } 10000+4 \% \text { of }(x-10000)]=31100 \\ & \Leftrightarrow x-\left[\frac{5}{100} \times 10000+\frac{4}{100}(x-10000)\right]=31100 \\ & \Leftrightarrow x-500-\left(\frac{x-10000}{25}\right)=31100 \\ & \Leftrightarrow x-\frac{x}{25}=31200 \Leftrightarrow \frac{24 x}{25}=31200 \\ & \Leftrightarrow x=\left(\frac{31200 \times 25}{24}\right)=32500 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.