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Rachel is a fashion designer who bought two dresses for Rs. 60000 and design them in her own way. She then sold the first at 5% profit and the second at 47% profit. If the selling price of both dresses is same, then the difference of the cost price of the two dresses was

Rachel is a fashion designer who bought two dresses for Rs. 60000 and design them in her own way. She then sold the first at 5% profit and the second at 47% profit. If the selling price of both dresses is same, then the difference of the cost price of the two dresses was Correct Answer Rs. 10000

Given:

Cost price of both dresses = Rs. 60000

Profit on first dress = 5%

Profit on second dress = 47%

Selling price of first dress = Selling price of second dress

Formula Used:

Profit % = ((SP - CP)/CP) × 100%

Calculation:

Let the cost price of first dress = Rs. x

and the cost price of second dress = Rs. y

Let the selling price of each dress = Rs. z

Profit on first dress = 5%

Profit % = ((SP - CP)/CP) × 100%

⇒ 5 = ((z - x)/x) × 100

⇒ 1/20 = (z - x)/x

⇒ x = 20(z - x)

⇒ x = 20z - 20x

⇒ 21x = 20z

⇒ x = (20/21)z

Profit on second dress = 47%

Profit % = ((SP - CP)/CP) × 100%

⇒ 47 = ((z - y)/y) × 100

⇒ 47y = 100(z - y)

⇒ 47y = 100z - 100y

⇒ 147y = 100z

⇒ y = (100/147)z

∵ x + y = 60000

(20/21)z + (100/147)z = 60000

⇒ (5040/3087)z = 60000

⇒ z = 36750

∴ Selling price of each dress = Rs. 36750

x = (20/21)z

⇒ x = (20/21) × 36750

⇒ x = 35000

y = (100/147)z

⇒ y = (100/147) × 36750

⇒ y = 25000

The cost price of two dresses was Rs.35000 and Rs.25000 respectively.

∴ The difference of the cost price of the two dresses was Rs.10000.

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