Direct and Inverse Proportion Class 8 Worksheets — Free CBSE PDF with Answers

This direct and inverse proportion Class 8 worksheet follows the NCERT Chapter 13 syllabus and covers both direct proportion and inverse proportion with worked word problems. Every question has a step-by-step solution and is printable as a free PDF.

Two quantities are in direct proportion when they increase or decrease together in the same ratio — if one doubles, the other doubles. Two quantities are in inverse proportion when one increases as the other decreases in the same ratio — if the number of workers doubles, the hours needed halves. This worksheet gives students 30 practice questions split across both types, at easy, medium, and hard difficulty, so they can build fluency with the classic Class 8 CBSE question patterns.

Typical questions include finding the cost of rice given price for a different quantity, figuring out how long workers take to finish a job, and problems where vehicles cover the same distance at different speeds (km/hr). These are the exact setups rivals rank for — and the ones your Class 8 exam tests.

In a direct proportion problem, you know three quantities and need to find the fourth. The rule is simple: if $\frac{x_1}{y_1} = \frac{x_2}{y_2}$, then $x_1 y_2 = x_2 y_1$. Cross-multiply and solve for the unknown.

Example: If 5 kg of rice costs ₹250, find the cost of 12 kg of rice. Setup: cost is directly proportional to weight. So $\frac{250}{5} = \frac{x}{12}$, which gives $x = \frac{250 \times 12}{5} = ₹600$. A 12 kg bag costs ₹600.

Another classic: A car travels 60 km in 1 hour. How far will it cover in 3.5 hours at the same speed? Direct proportion gives $60 \times 3.5 = 210$ km. When two vehicles cover the same distance at the same speed, time and distance are directly proportional.

In an inverse proportion problem, as one quantity increases the other decreases — but their product stays constant. The rule: $x_1 \times y_1 = x_2 \times y_2$. Multiply the known pair, then divide by the new value.

Example: 15 workers can build a wall in 48 hours. How many workers are needed to build the same wall in 30 hours? Setup: numbers of workers and time are inversely proportional. So $15 \times 48 = x \times 30$, giving $x = \frac{720}{30} = 24$ workers. You need 24 workers to finish in 30 hours.

Another: A car covers a distance at 60 km/hr in 4 hours. How long will it take at 80 km/hr to cover the same distance? Speed and time are inversely proportional when distance is fixed. So $60 \times 4 = 80 \times t$, giving $t = 3$ hours.

Try these extra questions in your notebook before checking the answers in the PDF. Each one mirrors the style of a CBSE Class 8 exam question and uses the same language your textbook uses.

1. If 9 kg of rice costs ₹540, find the cost of 14 kg of the same rice. 2. A car running at 45 km/hr covers a distance in 6 hours. How long will the car take at 54 km/hr to cover the same distance? 3. 20 workers can complete a task in 12 days. How many days will 30 workers take to complete the same task? 4. If the cost of 15 notebooks is ₹375, find the cost of 24 notebooks. 5. A train takes 8 hours to reach a station at 60 km/hr. How fast must it go to reach in 6 hours? 6. 8 taps fill a tank in 27 minutes. How long will 12 taps of the same type take?

The worksheet PDF contains 30 fully-solved practice questions spanning all of the above scenarios, plus multi-step problems that combine direct and inverse proportion.

The trick is to read the question and ask: as one quantity grows, does the other grow or shrink? If both grow together (more kg → more cost, more hours → more distance), it's direct proportion. If one grows while the other shrinks (more workers → less time, higher speed → less time), it's inverse proportion.

A simple table helps. Write the known value in one column, the unknown in another, and underneath each write whether it increases or decreases. If both arrows point the same way, use direct. If they point opposite ways, use inverse. This is the same technique CBSE Class 8 textbooks use and it works on every exam question.