TalentJR Tools

Ratio and Proportion Calculator

Simplify any ratio to its lowest terms, find the missing value in a proportion, or split an amount in a given ratio — for sharing money, mixing ingredients or solving textbook problems. Each answer shows the working.

Separate terms with a colon (:)

Simplest form
3 : 4
Step-by-step solution
  1. HCF of 45, 60 = 15
  2. Divide each term by 15 → 3 : 4

How to use the ratio calculator

  1. Choose a mode: "Simplify ratio", "Solve proportion" or "Divide in ratio".
  2. Enter the ratio using colons (e.g. 2:3:5) or the values A, B and C.
  3. See the answer and the steps used to find it.

Formulas

Simplest forma : b = (a ÷ HCF) : (b ÷ HCF)
Proportiona : b = c : x ⇒ x = (b × c) ÷ a
Product of extremes = product of means.
Divide N in ratio a : bShare₁ = N × a/(a + b), Share₂ = N × b/(a + b)

Solved examples

Example 1: Simplify 45 : 60.

  • HCF of 45 and 60 = 15
  • 45 ÷ 15 : 60 ÷ 15

Answer: 3 : 4

Example 2: If 4 pens cost ₹60, how much do 7 pens cost?

  • 4 : 60 = 7 : x
  • x = 60 × 7 ÷ 4

Answer: ₹105

Example 3: Divide ₹12,000 among three friends in the ratio 2 : 3 : 5.

  • Sum of parts = 10
  • Shares = 12,000 × 2/10, × 3/10, × 5/10

Answer: ₹2,400, ₹3,600, ₹6,000

Ratio vs. proportion

A ratio compares two quantities of the same kind by division — 3 boys to 4 girls is written 3 : 4. A proportion states that two ratios are equal, such as 3 : 4 = 9 : 12. Ratios have no units, so always convert both quantities into the same unit (for example, both in centimetres) before comparing them.

Using the unitary method

The unitary method solves proportion problems in two steps: find the value of one unit, then multiply. If 4 pens cost ₹60, one pen costs ₹15, so 7 pens cost ₹105. The proportion solver on this page gives the same answer using cross-multiplication.

In exams, partnership, mixture and alligation, and age problems are all ratio problems in disguise.

📘 Learn it in your NCERT syllabus

Free chapter notes, flashcards and quizzes on TalentJR CBSE.

🎯 Asked in competitive exams

This topic regularly appears in the quantitative aptitude section of:

  • SSC CGL & CHSL
  • IBPS & SBI PO / Clerk
  • RRB NTPC
  • Campus placement aptitude tests
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Frequently asked questions

How do I simplify a ratio?

Find the HCF of all the terms and divide each term by it. For 12 : 18, the HCF is 6, so the simplest form is 2 : 3.

How do I simplify a ratio with decimals?

Multiply all terms by a power of 10 to remove the decimals, then divide by the HCF. 1.5 : 2.25 becomes 150 : 225, which simplifies to 2 : 3.

How do I divide money in a ratio?

Add the parts of the ratio, then multiply the total by each part divided by the sum. ₹1,000 in the ratio 2 : 3 gives ₹400 and ₹600.

Can a ratio have more than two terms?

Yes. Ratios like 2 : 3 : 5 are common in partnership and mixture problems. This calculator simplifies and divides ratios with up to 10 terms.

What is cross-multiplication?

In a : b = c : d, the product of the extremes (a × d) equals the product of the means (b × c). This lets you find any one missing term.

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