High School

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1. A trader allows two successive discounts of 20% and 10%. If he gets Rs. 108 for an article, find its marked price.
- a) Rs. 140
- b) Rs. 150
- c) Rs. 160
- d) Rs. 170

2. A dishonest merchant professes to sell his goods at cost price but uses a weight of 900 grams for one kg weight. What is his profit percentage?
- a) 10%
- b) 9.09%
- c) 11.11%
- d) 16.67%

3. If the profit made by a trader is one-fifth of the SP, find the actual profit percentage.
- a) 30%
- b) 20%
- c) 25%
- d) None of these

4. By selling 60 mangoes, a fruit seller gains the selling price of 20 mangoes. Find his gain percentage.
- a) 30%
- b) 40%
- c) 50%
- d) 25%

5. By selling 14 oranges for a rupee, a man loses 12%. How many should he sell for a rupee to gain 12%?
- a) 9
- b) 12
- c) 10
- d) 11

6. A fruit seller bought 1800 oranges at Rs. 70 per dozen. 12% of these were found spoiled and unfit to be sold. At what price per dozen should he sell the remaining to gain 10% overall?
- a) Rs. 85.4
- b) Rs. 87.5
- c) Rs. 90
- d) Rs. 86

7. On selling a bag for Rs. 432, a man gains 20%. What price should he mark on the bag to please the customer by offering a 10% discount and still earn 25% in the transaction?
- a) Rs. 437
- b) Rs. 450
- c) Rs. 500
- d) Rs. 525

8. On selling 60 notebooks, Rohan gained the cost price of 15 notebooks. What is his profit percentage?
- a) 20%
- b) 25%
- c) 33 1/3%
- d) 50%

9. A trader allows a discount of 20% for cash payment. How much percent above the cost price must he mark his goods to make a profit of 20%?
- a) 25%
- b) 50%
- c) 30%
- d) 40%

10. A shopkeeper professes to sell his goods at cost price. However, he uses a faulty balance that balances 960 gm of tomatoes with a 1 kg weight. What percentage of profit or loss will he incur?
- a) 4.16% profit
- b) 5.25% profit
- c) 4.16% loss
- d) 5.25% loss

Answer :

Let's solve each problem one by one:

  1. Finding the marked price of an article with successive discounts

    The trader gives two successive discounts of 20% and 10% on the marked price.

    Let's assume the marked price is [tex]x[/tex].

    After the first discount of 20%, the price becomes [tex]0.8x[/tex].

    After the second discount of 10%, the price becomes [tex]0.9 \times 0.8x = 0.72x[/tex].

    The final amount the trader receives is Rs.108.

    So, [tex]0.72x = 108[/tex].

    Solving for [tex]x[/tex]:

    [tex]x = \frac{108}{0.72} = 150[/tex]

    Therefore, the marked price of the article is Rs.150.

  2. Calculating the profit percentage for a dishonest merchant

    The merchant uses 900 grams instead of 1 kilogram (1000 grams).

    The true cost should be based on 1 kg, but he gains 100 grams on every kg sold.

    The effective weight sold is 900 grams, where he makes a profit on the missing 100 grams out of 1000 grams.

    Therefore, the profit percentage [tex]P[/tex] is calculated by:

    [tex]P = \frac{100}{900} \times 100\% = 11.11\%[/tex]

    Hence, the profit percentage is 11.11%.

  3. Finding the actual profit percentage when profit is one-fifth of the selling price (SP)

    Let the selling price be [tex]SP[/tex].

    Profit is [tex]\frac{1}{5} \times SP[/tex].

    Therefore, [tex]SP = CP + \frac{SP}{5}[/tex], where [tex]CP[/tex] is the cost price.

    Solving, [tex]CP = \frac{4}{5}SP[/tex].

    Profit percentage is:

    [tex]P\% = \left( \frac{SP - CP}{CP} \right) \times 100\%[/tex]

    [tex]P\% = \left( \frac{SP - \frac{4}{5}SP}{\frac{4}{5}SP} \right) \times 100\% = 25\%[/tex]

    Therefore, the actual profit percentage is 25%.

These explanations step through the processes needed to solve each problem, employing basic principles of percentage calculations and algebra. By understanding these solutions, students can apply similar methods to a wide variety of related problems.

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Rewritten by : Barada