Question

A high-end watch is initially marked up by 50% above its cost price. During a sale, it is offered at a discount of 20% on its marked price. However, a special customer receives an additional discount of y% on the discounted price, bringing the final selling price to ₹4320. If the shopkeeper still makes a profit of 8% on the cost price after all discounts, what was the original cost price of the watch and the value of y?

• A. CP = ₹4000 , y = 10%
• B. CP = ₹4500 , y = 10%
• C. CP = ₹4800 , y = 5%
• D. CP = ₹5000 , y = 8%

Answer 1

Answer:

A. CP = ₹4000 , y = 10%

Let the cost price (CP) of the watch be (x).

Step 1: Marked Price (MP)

The watch is marked up by 50%:

MP = 1.5x

Step 2: After 20% discount

Selling price after the first discount:

$= 1.5x \times 0.8 = 1.2x$

Step 3: After additional (y%) discount

Final selling price is ₹4320:

$1.2x\left(1-\frac{y}{100}\right)=4320$

Step 4: Use the profit condition

The shopkeeper still earns 8% profit:

SP = 1.08x

Since the final SP is ₹4320,

1.08x=4320

$x=\frac{4320}{1.08}=4000$

So, the original cost price = ₹4000.

Step 5: Find (y)

Substitute (x=4000):

$1.2(4000)\left(1-\frac{y}{100}\right)=4320$

$4800\left(1-\frac{y}{100}\right)=4320$

$1-\frac{y}{100}=\frac{4320}{4800}=0.9$

$\frac{y}{100}=0.1$

$\boxed{y=10\%}$

Final Answer

• Original Cost Price = ₹4000

• $Additional Discount = (\boxed{10\%})$