a book is sold at 10% loss. If the book was bought at 20% less and sold at 44 more he would gain 40%. what was the cost price?

Let the cost price of the book be $ C $.

### Step 1: Selling at a 10% loss
The selling price (S.P.) in this case is 10% less than the cost price:
\[
S.P. = C - 0.1C = 0.9C
\]

### Step 2: Alternative scenario where there's a 40% gain
In this scenario, the cost price is 20% less, so the new cost price is:
\[
\text{New cost price} = C - 0.2C = 0.8C
\]

In this case, the selling price is 40% more than the new cost price. So, the new selling price would be:
\[
\text{New selling price} = 0.8C + 0.4(0.8C) = 0.8C(1 + 0.4) = 1.12C
\]

### Step 3: Relating the two selling prices
The new selling price is $44 more than the original selling price:
\[
1.12C = 0.9C + 44
\]

### Step 4: Solving for $ C $
\[
1.12C - 0.9C = 44
\]
\[
0.22C = 44
\]
\[
C = \frac{44}{0.22} = 200
\]

Thus, the cost price of the book is $ C = 200 $.

Would you like further explanation or have any questions?

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Here are 5 related questions to explore:

1. How would the problem change if the loss was 15% instead of 10%?
2. What would be the new selling price if the book was sold at a 20% profit?
3. How does percentage gain or loss relate to changes in cost price?
4. If the book was sold at a 25% loss, what would be the new selling price?
5. What happens to the profit margin if the cost price increases by 50%?

**Tip:** Always convert percentages into decimals for easier calculations!

A book is sold at 10% loss. If the book was bought at 20% less and sold at $44 more, he would gain 40%. What was the cost price?

Solve a detailed profit and loss problem where a book is sold at 10% loss. If the book was bought 20% cheaper and sold at $44 more, the seller would gain 40%. Learn the step-by-step process to find the cost price, with formulas and key concepts from percentages and algebra. Suitable for Grades 8-10.

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