In September 2009, the sales of a product were $\frac{2}{3} \mathrm{rd}$ of that in July 2009. In November 2009, the sales of the product were higher by 5\% as compared to September 2009. How much is the percentage of increase in sales in November 2009 with respect to the base figure in July 2009?
(a)- 20\%
(b)25\%
(c)- 30\%
(d)+ 40\%
Answer
Answer (as printed): C
Explanation
Let the total sales in July 2009 be ₹ $x$. Then, sales in September $2009=₹ \frac{2 x}{3}$. Sales in November $2009=105 \%$ of $₹ \frac{2 x}{3}$ $$=₹\left(\frac{105}{100} \times \frac{2 x}{3}\right)=₹ \frac{7 x}{10} .$$ Decrease in sales $=₹\left(x-\frac{7 x}{10}\right)=₹ \frac{3 x}{10}$ $$\text { ∴ Decrease } \%=\left(\frac{3 x}{10} \times \frac{1}{x} \times 100\right) \%=30 \% \text {. }$$
Explanation as extracted from the printed page; notation may be imperfect.