Question:
An article is sold for ₹ 351.90 after giving two successive discounts of \(x\ \%\) and 15% on its marked price of ₹ 450. If a single discount of \(2x\ \%\) is given on its marked price, then its selling price will be:
किसी वस्तु को उसके अंकित मूल्य ₹ 450 पर \(x\ \%\) और 15% की दो क्रमिक छूट देने के बाद ₹ 351.90 में बेचा जाता है। यदि उसके अंकित मूल्य पर \(2x\ \%\) की एक एकल छूट दी जाए, तो उसका विक्रय मूल्य क्या होगा?
Options:
- ₹ 387.50
- ₹ 360
- ₹ 378
- ₹ 382.50
- ₹ 387.50
- ₹ 360
- ₹ 378
- ₹ 382.50
Correct Answer: c)
Explanation:
Step 1: Determine the value of \(x\):
Marked Price \(MP = ₹ 450\).
After a 15% discount, the price becomes:
\[ 450 \times (1 – 0.15) = 450 \times 0.85 = ₹ 382.50 \]
After giving a further discount of \(x\%\), the final selling price is ₹ 351.90:
\[ 382.50 \times \left(1 – \frac{x}{100}\right) = 351.90 \]
\[ 1 – \frac{x}{100} = \frac{351.90}{382.50} = \frac{3519}{3825} = \frac{391}{425} = \frac{23}{25} = 0.92 \]
\[ \frac{x}{100} = 1 – 0.92 = 0.08 \implies x = 8 \]
Thus, \(x = 8\%\).
Step 2: Calculate the selling price with a single discount of \(2x\%\):
\[ \text{Discount percentage} = 2x\% = 2 \times 8\% = 16\% \]
\[ \text{Selling Price} = MP \times (1 – 0.16) = 450 \times 0.84 = ₹ 378 \]
Hence, the correct answer is option c).
चरण 1: \(x\) का मान ज्ञात करें:
अंकित मूल्य \(MP = ₹ 450\)।
15% की छूट के बाद मूल्य:
\[ 450 \times 0.85 = ₹ 382.50 \]
अब \(x\%\) की छूट देने के बाद विक्रय मूल्य ₹ 351.90 है:
\[ 382.50 \times \left(1 – \frac{x}{100}\right) = 351.90 \]
\[ 1 – \frac{x}{100} = \frac{351.90}{382.50} = 0.92 \]
\[ \frac{x}{100} = 0.08 \implies x = 8 \]
अतः \(x = 8\%\) है।
चरण 2: \(2x\%\) की एकल छूट पर विक्रय मूल्य ज्ञात करें:
\[ \text{छूट} = 2x\% = 2 \times 8\% = 16\% \]
\[ \text{विक्रय मूल्य} = 450 \times (1 – 0.16) = 450 \times 0.84 = ₹ 378 \]
अतः सही उत्तर विकल्प c) है।