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Proportion Calculator: Direct and Inverse

Type a known pair and the new quantity. Choose direct (both go up together) or inverse (one goes up, the other goes down).

Answer (y₂)

96

Value for 1 unit (y ÷ x)
12
Proportion
60/5 = 96/8

Direct: both go up together, e.g. more pens → more cost.

Show working
  1. y₁ ÷ x₁ = y₂ ÷ x₂
  2. 60 ÷ 5 = 12
  3. y₂ = 12 × 8 = 96

How to use

  1. Choose Direct or Inverse.
  2. Type the first quantity and its value, for example 5 pens and ₹60.
  3. Type the new quantity and read the answer with the steps.

Good to know

Direct proportion: y ÷ x stays the same. Find the value of one unit and multiply: 5 pens cost ₹60, so 1 pen costs ₹12 and 8 pens cost ₹96. Cost and quantity, distance and time at a fixed speed, and wages and days worked are usually direct.

Inverse proportion: x × y stays the same. 6 workers finish a job in 10 days, so the job is 60 worker-days, and 4 workers need 60 ÷ 4 = 15 days. Speed and travel time for a fixed distance, and workers and days for a fixed job, are usually inverse.

Real situations are only roughly proportional: bulk discounts, fixed charges and people working at different speeds all break the rule. Check that doubling one quantity really doubles (or halves) the other before trusting the answer.

Questions

What is the unitary method?

Find the value of one unit first, then multiply by the number of units you need. It is how NCERT teaches direct and inverse proportion.

How do I know if it is direct or inverse?

Ask: if one doubles, does the other double (direct) or halve (inverse)? More items cost more (direct); more workers take fewer days (inverse).

If 12 workers build a wall in 8 days, how long will 16 take?

12 × 8 = 96 worker-days, and 96 ÷ 16 = 6 days. Choose Inverse with 12, 8 and 16.

If a car goes 150 km on 10 litres, how far on 25 litres?

Direct: 150 ÷ 10 = 15 km per litre, so 25 litres go 375 km.

What is the difference between ratio and proportion?

A ratio compares two quantities (3 : 4). A proportion says two ratios are equal (3 : 4 = 9 : 12).

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