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Math  /  Numbers & Operations

Question8. a) A stationer buys 1 dozen of pens at Rs 20 each and sells them at Rs 25 each. (ii) Find the cost price and selling price of 1 dozen of pens. (ii) How much profit does he make in 1 dozen of pens. (iii) Express his profit into profit percent. (iv) If he had given Re 1 discount in each pen, what would be his profit percent? b) A grocer purchased 5 dozen of eggs at Rs 12 each. 10 eggs were broken and he sold the remaining eggs at Rs 14 each. (i) Find the cost price of total number of eggs and the selling price of the remaining number of eggs. (ii) Calculate his profit or loss and express it in percent. (iii) If non of the eggs were broken, how much profit or loss percent would he make? c) A fruit seller sold 50 kg of oranges at the rate of Rs 80 per kg and gained Rs 800. (i) Find the selling price of 50 kg of oranges. (ii) At what rate of price did he buy the oranges? (iii) Calculate his profit percent.
1 kg d) A vegetable seller purchased 1 quintal of potatoes at Rs 35 per kg and sold at a loss of Rs 350\mathbf{3 5 0}. Find: (i) the rate of selling price (ii) Loss percent.

Studdy Solution

STEP 1

1. The cost price (CP) and selling price (SP) are calculated for a dozen or total quantity as specified.
2. Profit or loss is calculated as the difference between SP and CP.
3. Profit or loss percent is calculated based on CP.
4. Discounts affect the selling price directly.

STEP 2

1. Solve part (a) related to pens.
2. Solve part (b) related to eggs.
3. Solve part (c) related to oranges.
4. Solve part (d) related to potatoes.

STEP 3

a) (i) Calculate the cost price and selling price of 1 dozen pens.
Cost price of 1 dozen pens: CP per pen=Rs 20\text{CP per pen} = \text{Rs } 20 CP of 1 dozen=12×20=Rs 240\text{CP of 1 dozen} = 12 \times 20 = \text{Rs } 240
Selling price of 1 dozen pens: SP per pen=Rs 25\text{SP per pen} = \text{Rs } 25 SP of 1 dozen=12×25=Rs 300\text{SP of 1 dozen} = 12 \times 25 = \text{Rs } 300

STEP 4

a) (ii) Calculate the profit for 1 dozen pens.
Profit: Profit=SP of 1 dozen−CP of 1 dozen=300−240=Rs 60\text{Profit} = \text{SP of 1 dozen} - \text{CP of 1 dozen} = 300 - 240 = \text{Rs } 60

STEP 5

a) (iii) Calculate the profit percent for 1 dozen pens.
Profit percent: Profit Percent=(ProfitCP of 1 dozen)×100=(60240)×100=25%\text{Profit Percent} = \left(\frac{\text{Profit}}{\text{CP of 1 dozen}}\right) \times 100 = \left(\frac{60}{240}\right) \times 100 = 25\%

STEP 6

a) (iv) Calculate the profit percent with a Re 1 discount per pen.
New SP per pen with discount: New SP per pen=25−1=Rs 24\text{New SP per pen} = 25 - 1 = \text{Rs } 24 New SP of 1 dozen: New SP of 1 dozen=12×24=Rs 288\text{New SP of 1 dozen} = 12 \times 24 = \text{Rs } 288
New Profit: New Profit=New SP of 1 dozen−CP of 1 dozen=288−240=Rs 48\text{New Profit} = \text{New SP of 1 dozen} - \text{CP of 1 dozen} = 288 - 240 = \text{Rs } 48
New Profit percent: New Profit Percent=(48240)×100=20%\text{New Profit Percent} = \left(\frac{48}{240}\right) \times 100 = 20\%

STEP 7

b) (i) Calculate the cost price and selling price for eggs.
Cost price of 5 dozen eggs: CP per egg=Rs 12\text{CP per egg} = \text{Rs } 12 Total CP=5×12×12=Rs 720\text{Total CP} = 5 \times 12 \times 12 = \text{Rs } 720
Selling price of remaining eggs: Remaining eggs=60−10=50\text{Remaining eggs} = 60 - 10 = 50 SP per egg=Rs 14\text{SP per egg} = \text{Rs } 14 Total SP=50×14=Rs 700\text{Total SP} = 50 \times 14 = \text{Rs } 700

STEP 8

b) (ii) Calculate profit or loss and express it in percent.
Loss: Loss=Total CP−Total SP=720−700=Rs 20\text{Loss} = \text{Total CP} - \text{Total SP} = 720 - 700 = \text{Rs } 20
Loss percent: Loss Percent=(20720)×100≈2.78%\text{Loss Percent} = \left(\frac{20}{720}\right) \times 100 \approx 2.78\%

STEP 9

b) (iii) Calculate profit or loss percent if no eggs were broken.
Total SP if no eggs were broken: Total SP=60×14=Rs 840\text{Total SP} = 60 \times 14 = \text{Rs } 840
Profit: Profit=Total SP−Total CP=840−720=Rs 120\text{Profit} = \text{Total SP} - \text{Total CP} = 840 - 720 = \text{Rs } 120
Profit percent: Profit Percent=(120720)×100=16.67%\text{Profit Percent} = \left(\frac{120}{720}\right) \times 100 = 16.67\%

STEP 10

c) (i) Calculate the selling price of 50 kg of oranges.
Selling price: SP=50×80=Rs 4000\text{SP} = 50 \times 80 = \text{Rs } 4000

STEP 11

c) (ii) Calculate the rate at which the oranges were bought.
Profit: Profit=Rs 800\text{Profit} = \text{Rs } 800
Cost price: CP=SP−Profit=4000−800=Rs 3200\text{CP} = \text{SP} - \text{Profit} = 4000 - 800 = \text{Rs } 3200
Rate of purchase: Rate per kg=320050=Rs 64\text{Rate per kg} = \frac{3200}{50} = \text{Rs } 64

STEP 12

c) (iii) Calculate the profit percent for oranges.
Profit percent: Profit Percent=(8003200)×100=25%\text{Profit Percent} = \left(\frac{800}{3200}\right) \times 100 = 25\%

STEP 13

d) (i) Calculate the rate of selling price for potatoes.
Total weight: Weight=1 quintal=100 kg\text{Weight} = 1 \text{ quintal} = 100 \text{ kg}
Cost price: CP per kg=Rs 35\text{CP per kg} = \text{Rs } 35 Total CP=100×35=Rs 3500\text{Total CP} = 100 \times 35 = \text{Rs } 3500
Loss: Loss=Rs 350\text{Loss} = \text{Rs } 350
Selling price: Total SP=Total CP−Loss=3500−350=Rs 3150\text{Total SP} = \text{Total CP} - \text{Loss} = 3500 - 350 = \text{Rs } 3150
Rate of selling price: Rate per kg=3150100=Rs 31.50\text{Rate per kg} = \frac{3150}{100} = \text{Rs } 31.50

STEP 14

d) (ii) Calculate the loss percent for potatoes.
Loss percent: Loss Percent=(3503500)×100=10%\text{Loss Percent} = \left(\frac{350}{3500}\right) \times 100 = 10\%

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