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