Percentage Problems Worksheet 4 | Worksheets | Math Center - Free Printable

Sure! Let’s solve each problem step by step with clear explanations.

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Problem 1.
*A car rides 150 km which is 75% of the road.*
a. How long is the road?
b. How many km are left?

✔ Solution:

Let the total length of the road = \( x \) km.

We’re told that 75% of \( x \) = 150 km.

So:
\[
0.75x = 150
\]

Divide both sides by 0.75:
\[
x = \frac{150}{0.75} = 200
\]

👉 a. The road is 200 km long.

Now, to find how much is left:
Total – traveled = 200 – 150 = 50 km

👉 b. 50 km are left.

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Problem 2.
*Damaged goods are sold for 35% of its price. What would be the original price of the goods if it was sold for $17,500?*

✔ Solution:

Let the original price = \( x \).

Sold for 35% of original → \( 0.35x = 17,500 \)

Solve for \( x \):
\[
x = \frac{17,500}{0.35} = 50,000
\]

👉 Original price = $50,000

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Problem 3.
*A car was sold for $63,750 after a discount of 15%.*
a. What was the price before discount?
b. What was the discount amount?

✔ Solution:

If there’s a 15% discount, then the selling price is 85% of the original price.

Let original price = \( x \)

Then:
\[
0.85x = 63,750
\]

Solve for \( x \):
\[
x = \frac{63,750}{0.85} = 75,000
\]

👉 a. Price before discount = $75,000

Discount amount = Original – Sale price = 75,000 – 63,750 = $11,250

👉 b. Discount amount = $11,250

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Problem 4.
*The price of a piece of furniture was raised by 10% and it was sold for $5500.*
a. What was the price before the increase?
b. How much did the price raise?

✔ Solution:

Let original price = \( x \)

After 10% increase → new price = \( 1.10x = 5500 \)

Solve for \( x \):
\[
x = \frac{5500}{1.10} = 5000
\]

👉 a. Price before increase = $5,000

Price raise = 5500 – 5000 = $500

👉 b. Price raised by $500

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Problem 5.
*A rope was cut short by 0.4 of its length, and the remaining rope is 1½ meters long. What was the original length?*

✔ Solution:

Cutting off 0.4 (which is 40%) means 60% remains.

Remaining length = 1.5 meters = 60% of original.

Let original length = \( x \)

Then:
\[
0.60x = 1.5
\]

Solve for \( x \):
\[
x = \frac{1.5}{0.6} = 2.5
\]

👉 Original length = 2.5 meters

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Problem 6.
*A product price was raised by 250%.*
a. By what times was the price increased?
b. What was the original price if the current price is $17,500?

✔ Solution:

a. “Raised by 250%” means the price became:

Original + 250% of original = 100% + 250% = 350% of original

So, the price is now 3.5 times the original.

👉 a. The price was increased by 3.5 times.

b. Current price = $17,500 = 3.5 × original price

Let original = \( x \)

\[
3.5x = 17,500
\]

\[
x = \frac{17,500}{3.5} = 5,000
\]

👉 b. Original price = $5,000

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## ✔ Final Answers Summary:

1.
a. 200 km
b. 50 km

2. $50,000

3.
a. $75,000
b. $11,250

4.
a. $5,000
b. $500

5. 2.5 meters

6.
a. 3.5 times
b. $5,000

Let me know if you’d like these explained in another way or need visual diagrams! 😊