Question

Given below are two statements:
Statement I : The difference between the cost price and sale price of an article is ₹ 240. If the profit is 20%, then the selling price is ₹ 1440. 
Statement II: If the cost price of 10 DVDs is equal to the selling price of 7 DVDs, then the gain percent is \(42\frac{6}{7}\).
In the light of the above statements, choose the most appropriate answer from the options given below:

• A. Both Statement I and Statement II are correct
• B. Both Statement I and Statement II are incorrect
• C. Statement I is correct but Statement II is incorrect
• D. Statement I is incorrect but Statemenent II is correct

Answer 1

The Correct Option is A

 Let's evaluate both statements to determine their accuracy. 

1. Statement I: The difference between the cost price (CP) and sale price (SP) of an article is ₹ 240. If the profit is 20%, then the selling price is ₹ 1440.
   • We know that: \(SP = CP + \text{{Profit}}\).
   • Given that the profit is 20%, we can express this as \(SP = CP + 0.2 \times CP = 1.2 \times CP\).
   • Also, we know that the difference between SP and CP is ₹240, so \(SP - CP = ₹240\).
   • Substituting the expression for SP, we have: \(1.2 \times CP - CP = ₹240\).
   • This simplifies to \(0.2 \times CP = ₹240\).
   • Solving for CP: \(CP = \frac{240}{0.2} = ₹1200\).
   • Substituting CP into the expression for SP: \(SP = 1.2 \times ₹1200 = ₹1440\).
   • This confirms Statement I is correct as the SP calculated is ₹1440.
2. Statement II: If the cost price of 10 DVDs is equal to the selling price of 7 DVDs, then the gain percent is \(42\frac{6}{7}\).
   • Let the Cost Price (CP) of one DVD be \(x\).
   • The cost price of 10 DVDs is \(10x\). The selling price of 7 DVDs is also \(10x\).
   • Let the Selling Price (SP) of one DVD be \(y\). Hence, \(7y = 10x\), which implies \(y = \frac{10}{7}x\).
   • The gain on one DVD = \(y - x = \frac{10}{7}x - x = \frac{3}{7}x\).
   • Gain percent = \(\left( \frac{\frac{3}{7}x}{x} \times 100 \right) \% = \left( \frac{3}{7} \times 100 \right) \%\).
   • This calculates to approximately \(42.857\), which is equivalent to \(42 \frac{6}{7}\%\).
   • Hence, Statement II is correct.

Both Statement I and Statement II are indeed correct. Thus, the correct answer is: "Both Statement I and Statement II are correct".