Question

What is the cost price of the watch?
Statements:
I. The watch is sold at a discount of \(20\%\) of the marked price.
II. The shopkeeper made a profit of \(60\%\) of the cost price.

• A. Statement I alone is sufficient
• B. Statement II alone is sufficient
• C. Both statements I and II together are sufficient
• D. Neither statement I nor statement II is sufficient

Answer 1

The Correct Option is A

Step 1: Analyze Statement I 

• The statement mentions that the watch is sold at a 20% discount on the marked price.
• However, this does not provide any direct information about the cost price (C.P.), as we do not know the marked price or the selling price (S.P.).
• Conclusion: Statement I alone is insufficient.

Step 2: Analyze Statement II

• The statement mentions that the shopkeeper made a 60% profit on the cost price.
• This means the selling price (S.P.) can be expressed as:

\(S.P. = C.P. + 60% \times C.P. = 1.6 \times C.P.\)

• However, since we do not have any numerical value of the selling price, this equation does not help us find the exact value of the cost price.
• Conclusion: Statement II alone is insufficient.

Step 3: Combine Both Statements

• Statement I gives information about the discount on the marked price, but does not provide a relation between the cost price and the selling price.
• Statement II gives a relation between the selling price and the cost price but does not mention the marked price or discount in relation to the cost price.
• Since neither statement provides a direct equation to solve for the cost price, even when combined, they are still insufficient.

Final Conclusion

Neither Statement I nor Statement II is sufficient to determine the cost price.