Garima purchased a briefcase with an additional 10% discount on the reduced price after deducting 20% on the labelled price. If the labelled price was ₹ 1400, at what price did she purchase the briefcase?

### Concept & Successive Discounts When multiple discounts are given successively, each subsequent discount is applied to the new reduced price, not the original labelled price. $$ \text{Final Price} = \text{Labelled Price} \times \left(1 - \frac{D_1}{100}\right) \times \left(1 - \frac{D_2}{100}\right) $$ ### Step-by-Step Solution * Labelled price of the briefcase = ₹ 1400. * First discount is $20\%$ on the labelled price. * Price after first discount = $1400 \times \left(1 - 0.20\right) = 1400 \times 0.80 = 1120$. * An additional second discount of $10\%$ is given on this reduced price. * Final purchase price = $1120 \times \left(1 - 0.10\right) = 1120 \times 0.90$. * Final purchase price = $1120 \times \frac{90}{100} = 112 \times 9 = 1008$. ### Exam Strategy & Shortcut Use fractional multipliers for speed. A $20\%$ discount leaves $\frac{4}{5}$ of the price. A $10\%$ discount leaves $\frac{9}{10}$ of the price. Final Price = $1400 \times \frac{4}{5} \times \frac{9}{10} = 1400 \times \frac{36}{50} = 28 \times 36$. Since $28 \times 36$: units digit must be $8 \times 6 = 48 \implies 8$. Both 1008 and 980 are options, so compute $28 \times (30 + 6) = 840 + 168 = 1008$. ### Common Pitfall Adding the successive discount percentages together ($20\% + 10\% = 30\%$) and applying it as a single discount to the labelled price, which would incorrectly give $1400 \times 0.70 = 980$. ### Final Answer Therefore, the correct answer is **₹ 1008**.