Mehak bought two dresses for a certain amount. She sold the 1st dress at 30% profit and the other dress at 10% loss. In whole deal, she gained Rs. 120. If she had sold the second dress at 20% loss she would have no profit/loss. What is the cost of the 1st dress?

Mehak bought two dresses for a certain amount. She sold the 1st dress at 30% profit and the other dress at 10% loss. In whole deal, she gained Rs. 120. If she had sold the second dress at 20% loss she would have no profit/loss. What is the cost of the 1st dress? Correct Answer Rs. 800

Let, cost of the 1st dress be Rs. 100x and cost of the 2nd dress be Rs. 100y

⇒ SP of the 1st dress = Rs. 100x(1 + 30/100) = Rs. 130x

⇒ SP of the 2nd dress = Rs. 100y(1 – 10/100) = Rs. 90y

⇒ SP of the 2nd dress if sold at 20% loss = Rs. 100y(1 – 20/100) = Rs. 80y

According to the question,

(130x + 90y) – (100x + 100y) = 120

⇒ 30x – 10y = 120

⇒ 3x – y = 12 …… (1)

Now,

(130x + 80y) – (100x + 100y) = 0

⇒ 30x – 20y = 0

⇒ 3x – 2y = 0 …… (2)

From (2) – (1) we get,

y = 12

Putting y = 12 in (1) we get,

3x – 12 = 12

⇒ 3x = 24

⇒ x = 8

∴ Cost of the 1st dress = 100 × 8 = Rs 800

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