Multiple choice

Harman buys two dresses for a total cost of Rs. 900. By selling one dress for 4/5 of its cost price and the other for 5/4 of its cost price, she makes a profit of Rs. 90 on the whole transaction. The cost of the lower-priced dress is

  1. Rs. 300

  2. Rs. 400

  3. Rs. 350

  4. Rs. 450

  5. Rs. 250
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x and y be the costs. x+y=900. Profit = (5/4)y - y + (4/5)x - x = 90. (1/4)y - (1/5)x = 90. Multiply by 20: 5y - 4x = 1800. Substitute x = 900-y: 5y - 4(900-y) = 1800. 5y - 3600 + 4y = 1800. 9y = 5400. y = 600. Then x = 300. The lower-priced dress is 300.

AI explanation

Let the cost price of the first dress be x, making the cost price of the second dress (900 - x). The selling prices are 4/5 x and 5/4 (900 - x), giving the equation 4/5 x + 5/4 (900 - x) = 900 + 90. Solving 0.8x + 1125 - 1.25x = 990 yields 0.45x = 135. Therefore, x = 300, and since the other dress costs Rs. 600, the lower-priced dress is Rs. 300.

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