Worksheet-1 on Application of Percentage featuring eight multiple-choice questions involving real-life scenarios like buying and selling items, calculating profit and loss percentages.

Let's solve each question step-by-step and explain the reasoning behind the solutions.

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(1) Rahul purchased a cycle for Rs. 800 and sold it for Rs. 1040. Find his gain percent.

Given:
- Cost Price (CP) = Rs. 800
- Selling Price (SP) = Rs. 1040

Gain = SP - CP = 1040 - 800 = Rs. 240

Gain % = (Gain / CP) × 100 = (240 / 800) × 100 = 30%

✔ Answer: (B) 30%

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(2) Santosh bought a refrigerator for Rs. 9000 and was forced to sell it for Rs. 8100. Find the loss percent.

Given:
- CP = Rs. 9000
- SP = Rs. 8100

Loss = CP - SP = 9000 - 8100 = Rs. 900

Loss % = (Loss / CP) × 100 = (900 / 9000) × 100 = 10%

✔ Answer: (C) 10%

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(3) Oranges were bought at Rs. 36 per dozen and sold at the rate of Rs. 40 per 10. Find the gain or loss percent.

Step 1: Cost Price per orange
- 1 dozen = 12 oranges
- CP of 12 oranges = Rs. 36
- So, CP per orange = 36 / 12 = Rs. 3

Step 2: Selling Price per orange
- SP of 10 oranges = Rs. 40
- So, SP per orange = 40 / 10 = Rs. 4

Step 3: Gain per orange = 4 - 3 = Rs. 1

Gain % = (Gain / CP) × 100 = (1 / 3) × 100 = 33⅓%

✔ Answer: (A) 33⅓%

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(4) The cost price of 11 pencils is equal to the selling price of 10 pencils. Find the loss or gain percent.

Let the cost price of 1 pencil = Rs. 1
Then:
- CP of 11 pencils = Rs. 11
- SP of 10 pencils = Rs. 11 → So, SP of 1 pencil = 11 / 10 = Rs. 1.10

So:
- CP = Rs. 1
- SP = Rs. 1.10 → Profit

Profit = 1.10 - 1 = Rs. 0.10

Profit % = (0.10 / 1) × 100 = 10%

✔ Answer: (B) 10%

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(5) By selling a sari for Rs. 864, a shopkeeper earns a profit of 8%. Find the cost price.

We know:
- SP = Rs. 864
- Profit = 8%

Use formula:
> SP = CP × (1 + Profit%)
> 864 = CP × (1 + 0.08) = CP × 1.08

So,
> CP = 864 / 1.08 = 800

✔ Answer: (A) Rs. 800

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(6) Aman had to sell his television at a loss of 12%. If the selling price was Rs. 7040, what was its cost price?

Loss = 12%, SP = Rs. 7040

Formula:
> SP = CP × (1 - Loss%)
> 7040 = CP × (1 - 0.12) = CP × 0.88

So,
> CP = 7040 / 0.88 = 8000

✔ Answer: (B) Rs. 8000

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(7) Sanjay sold his old dining table set at a loss of 20%. If he had sold it for Rs. 800 more, he would have received a profit of 5%. Find the cost price.

Let CP = x

- At 20% loss: SP = x × (1 - 0.20) = 0.80x
- If sold for Rs. 800 more: SP = 0.80x + 800
- This gives 5% profit: SP = x × (1 + 0.05) = 1.05x

So:
> 0.80x + 800 = 1.05x
> 800 = 1.05x - 0.80x = 0.25x
> x = 800 / 0.25 = 3200

✔ Answer: (A) Rs. 3200

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(8) Ravi bought a second-hand car for Rs. 1,25,000 and spent Rs. 15,000 for repainting. If he sold it for Rs. 1,61,000, what is the profit percent?

Total Cost Price (CP):
- Purchase price = 1,25,000
- Repainting = 15,000
- Total CP = 1,25,000 + 15,000 = Rs. 1,40,000

Selling Price (SP) = Rs. 1,61,000

Profit = SP - CP = 1,61,000 - 1,40,000 = Rs. 21,000

Profit % = (Profit / CP) × 100 = (21,000 / 1,40,000) × 100 = 15%

✔ Answer: (D) 15%

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✔ Final Answers:

| Question | Answer |
|--------|--------|
| (1) | B (30%) |
| (2) | C (10%) |
| (3) | A (33⅓%) |
| (4) | B (10%) |
| (5) | A (Rs. 800) |
| (6) | B (Rs. 8000) |
| (7) | A (Rs. 3200) |
| (8) | D (15%) |

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