Find the cost price of a watch based on the following two statements:

I. A shopkeeper marks up the watch at Rs. 360 above the cost price and offers a 10\% discount on the marked price, resulting in an 8\% profit.

II. When the watch is sold at a 12\% profit, the difference between the selling price and the cost price is Rs. 216.

Using the information given, determine which of the following is true regarding the sufficiency of the statements to find the cost price of the watch.

Question

Find the cost price of a watch based on the following two statements:

I. A shopkeeper marks up the watch at Rs. 360 above the cost price and offers a 10\% discount on the marked price, resulting in an 8\% profit.

II. When the watch is sold at a 12\% profit, the difference between the selling price and the cost price is Rs. 216.

Using the information given, determine which of the following is true regarding the sufficiency of the statements to find the cost price of the watch.

Accepted Answer

**Solution:**

1. From statement (I):
   - Let the cost price be $ C $.
   - Marked price = $ C + 360 $.
   - Selling price after 10\% discount = $ $(C + 360) \times 0.9 $$.
   - Given profit is 8\%, so selling price = $$ C \times 1.08 $$.

Equate the two expressions for selling price:
   $$ (C + 360) \times 0.9 = 1.08C $$

Simplify:
   $$ 0.9C + 324 = 1.08C $$
   $$ 324 = 1.08C - 0.9C = 0.18C $$
   $$ C = \frac{324}{0.18} = 1800 $$

So, from statement (I) alone, cost price $ C = 1800 $.

2. From statement (II):
   - Profit = 12\% of cost price.
   - Profit amount = Selling price - Cost price = Rs. 216.

So,
   $$ 0.12C = 216 $$
   $$ C = \frac{216}{0.12} = 1800 $$

From statement (II) alone, cost price $ C = 1800 $.

3. Since both statements individually give the cost price as Rs. 1800, either statement alone is sufficient.

**Answer:** Either statement (I) or statement (II) alone is sufficient to find the cost price.

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