Profit Loss - All Subjects - Assignment - Teachmint - Free Printable

Let's solve each problem one by one with detailed explanations.

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4. Andy purchased 120 pencils at the rate of $2 per pencil. He sold 72 of them at the rate of $2.5 per pencil and the remaining at the rate of $2 per pencil. Find his profit or loss percent.

Step 1: Total Cost Price (C.P.)
- Number of pencils = 120
- Cost per pencil = $2
- Total C.P. = 120 × $2 = $240

Step 2: Selling Price (S.P.)
- Sold 72 pencils at $2.5 each:
- S.P.₁ = 72 × $2.5 = $180
- Remaining pencils = 120 – 72 = 48
- Sold at $2 each:
- S.P.₂ = 48 × $2 = $96
- Total S.P. = $180 + $96 = $276

Step 3: Profit
- Profit = S.P. – C.P. = $276 – $240 = $36

Step 4: Profit Percent
- Profit % = (Profit / C.P.) × 100 = (36 / 240) × 100 = 15%

✔ Answer: 15% profit

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5. Mike sold two horses for $18,000 each. On one he gained 20% and on the other he lost 20%. Find his total gain or loss.

Step 1: Let’s find C.P. of each horse

- First horse (20% gain):
- S.P. = $18,000
- Gain = 20%
- So, S.P. = C.P. × (1 + 20/100) = C.P. × 1.2
- C.P.₁ = 18,000 / 1.2 = $15,000

- Second horse (20% loss):
- S.P. = $18,000
- Loss = 20%
- S.P. = C.P. × (1 – 20/100) = C.P. × 0.8
- C.P.₂ = 18,000 / 0.8 = $22,500

Step 2: Total C.P. = $15,000 + $22,500 = $37,500
Total S.P. = $18,000 + $18,000 = $36,000

Step 3: Overall Loss
- Loss = C.P. – S.P. = $37,500 – $36,000 = $1,500
- Loss % = (Loss / Total C.P.) × 100 = (1,500 / 37,500) × 100 = 4%

✔ Answer: 4% loss

> 🔍 Note: When same S.P. is used and gain and loss percentages are equal, there is always a loss of (x²/100)% where x is the percentage. Here, x = 20 → Loss = (400)/100 = 4%.

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6. A television set was bought for $3900. $200 was spent on transportation and $900 on repair. It was sold at a loss of 10%. Find the S.P. of television.

Step 1: Total Cost Price (including overheads)
- Purchase price = $3900
- Transportation = $200
- Repair = $900
- Total C.P. = 3900 + 200 + 900 = $5000

Step 2: Sold at 10% loss
- Loss = 10% of $5000 = 0.10 × 5000 = $500
- S.P. = C.P. – Loss = 5000 – 500 = $4500

✔ Answer: $4500

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7. A bed sheet was sold for $483 thereby gaining 15%. Find the C.P. of the bed sheet.

We know:
- S.P. = $483
- Gain = 15%
- So, S.P. = C.P. × (1 + 15/100) = C.P. × 1.15

So,
- C.P. = 483 / 1.15 = $420

✔ Answer: $420

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8. Aaron bought an almirah for $1520 and sold it at a profit of 12½%. Find the selling price.

- Profit = 12½% = 12.5%
- C.P. = $1520
- S.P. = C.P. × (1 + 12.5/100) = 1520 × 1.125

Calculate:
- 1520 × 1.125 = 1520 × (1 + 0.125) = 1520 + (1520 × 0.125)
- 1520 × 0.125 = 1520 × 1/8 = 190
- So, S.P. = 1520 + 190 = $1710

✔ Answer: $1710

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9. By selling a camera for $2400, Ron loses 4%. At what price must he sell it to gain 12%?

Step 1: Find C.P. from loss scenario
- S.P. = $2400
- Loss = 4%
- So, S.P. = C.P. × (1 – 4/100) = C.P. × 0.96
- C.P. = 2400 / 0.96 = $2500

Step 2: To gain 12%, new S.P. = C.P. × (1 + 12/100) = 2500 × 1.12 = $2800

✔ Answer: $2800

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10. By selling a stool for $240 a carpenter loses 20%. How much per cent would he gain or lose by selling it for $360?

Step 1: Find C.P.
- S.P. = $240
- Loss = 20%
- So, S.P. = C.P. × 0.8
- C.P. = 240 / 0.8 = $300

Step 2: Now sell at $360
- S.P. = $360
- C.P. = $300
- Profit = 360 – 300 = $60
- Profit % = (60 / 300) × 100 = 20%

✔ Answer: 20% gain

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11. The selling price of 12 eggs is equal to the cost price of 15 eggs. Find the gain percent.

Let C.P. of 1 egg = $1 ⇒ C.P. of 15 eggs = $15
Then S.P. of 12 eggs = $15 ⇒ S.P. of 1 egg = 15 / 12 = $1.25

So:
- C.P. of 1 egg = $1
- S.P. of 1 egg = $1.25
- Profit per egg = $0.25
- Profit % = (0.25 / 1) × 100 = 25%

✔ Answer: 25% gain

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12. The cost price of 10 bananas is equal to the S.P. of 12 bananas. Find the loss percent.

Let C.P. of 1 banana = $1 ⇒ C.P. of 10 bananas = $10
This equals S.P. of 12 bananas ⇒ S.P. of 12 bananas = $10 ⇒ S.P. of 1 banana = 10 / 12 = $0.833...

Now:
- C.P. = $1
- S.P. = $0.833...
- Loss = 1 – 0.833... = $0.166...
- Loss % = (0.166... / 1) × 100 = (1/6) × 100 ≈ 16.67%

Or exactly:
- Loss % = (Loss / C.P.) × 100 = (1 - 10/12) / 1 × 100 = (2/12) × 100 = (1/6) × 100 = 16⅔%

✔ Answer: 16⅔% loss

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✔ Final Answers Summary:

| Question | Answer |
|--------|--------|
| 4 | 15% profit |
| 5 | 4% loss |
| 6 | $4500 |
| 7 | $420 |
| 8 | $1710 |
| 9 | $2800 |
| 10 | 20% gain |
| 11 | 25% gain |
| 12 | 16⅔% loss |

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