Ratio Calculator

Introduction to the Ratio Calculator

The Ratio Calculator handles four operations: simplify a:b to lowest terms by dividing both by HCF(a, b), scale a:b by factor k to get ka:kb, find missing value x in proportion a:b = c:x using cross-multiplication (x = bc/a), and convert ratio to percentage as a/(a+b) x 100% and (1 - a/(a+b)) x 100%.

Indian students from Class 6 onwards encounter ratios in NCERT chapter on Ratio and Proportion, then again in Class 7 on unitary method, Class 8 on direct and inverse proportion, and Class 10 on similar triangles. Ratios appear in CBSE board exams every year and dominate aptitude sections of CAT, SSC and bank PO exams.

You enter two or three terms (a, b or a, b, c) and choose operation. The calculator returns simplified form, scaled form, missing term, percentage split, decimal form a/b, and HCF used in simplification. It supports up to 4-term ratios for problems involving partnership profit-sharing or recipe scaling.

Who Should Use This Ratio Calculator

Class 6 and 7 students in Indore working on NCERT Ratio and Proportion problems use it to verify simplification homework and unitary method problems on prices and distances.

Class 10 CBSE students in Bengaluru applying ratios to similar triangles, trigonometry tan ratios, and probability sample space problems verify their solutions step-by-step.

CAT aspirants in Mumbai practicing partnership and profit-sharing problems with ratios like 2:3:5 split on Rs 50 lakh investment need quick scaling computations under exam pressure.

Bank PO and SSC candidates in Delhi tackling Quantitative Aptitude sections face 5-10 ratio questions per paper, where speed-solving via the calculator preview saves precious minutes.

Home cooks in Pune scaling Indian recipes (1:2 dal-to-water ratio, 1:1.5 rice-to-water for basmati) use ratio scaling to adapt 4-portion recipes to 6 or 8 portion family meals.

Tips for Ratio Problems

Smart Ratio Tips

Always simplify first by finding HCF. For 24:36, HCF is 12, so simplified is 2:3. This makes scaling and percentage conversion easier and matches the form expected in CBSE answer keys.

Use cross-multiplication for proportions: if a:b = c:d then ad = bc. So for 4:6 = x:24, x = 4 x 24 / 6 = 16. This single rule solves 80% of unitary method problems in NCERT and exams.

For three-term ratios like 2:3:5 used in partnership, convert to percentages: 20%, 30%, 50%. If total profit is Rs 1 lakh, shares are Rs 20,000, Rs 30,000, Rs 50,000. Verify by summing back to Rs 1 lakh.

For inverse proportion (more men, less time), invert one ratio. If 6 men complete work in 8 days, 4 men take 8 x 6/4 = 12 days. Common in CBSE Class 8 and SSC exams.

For Indian recipe scaling, treat ratios as multipliers. If a 1:2:3 (dal:rice:water) recipe serves 4, scaling to serve 6 means 1.5 cups dal, 3 cups rice, 4.5 cups water. The ratio is preserved.

Formula Explanation

Core Ratio Formulas

Simplified a:b = (a/HCF) : (b/HCF)

Scaled a:b by k = ka:kb

Proportion a:b = c:x means x = bc/a

Percentage of a in a:b = a/(a+b) x 100

Where:

• HCF = Highest Common Factor of a and b
• • k = scale factor (any positive number)
• • Cross product rule: ad = bc for a:b = c:d
• • Three-term: a/(a+b+c), b/(a+b+c), c/(a+b+c) percentages

Example: Simplify 48:64. HCF = 16. Simplified = 3:4. Scale by 5: 15:20. Percentage split: 3/(3+4) = 42.86%, 57.14%.

Common Ratios Quick Reference Table

Original Ratio	Simplified	Percent Split	Common Use
24:36	2:3	40%:60%	Boy-girl class
50:30:20	5:3:2	50%:30%:20%	Asset allocation
70:30	7:3	70%:30%	Equity-debt mix
1:1	1:1	50%:50%	Equal split
2:3:5	2:3:5	20%:30%:50%	Partnership
60:40	3:2	60%:40%	Marketing budget

Real-World Example

Example: Karan's Partnership Profit Sharing

Meet Karan, 34, a co-founder of a Mumbai-based logistics startup. He, Vikram and Anjali invested in the ratio 2:3:5 totalling Rs 1 crore (Karan Rs 20 lakh, Vikram Rs 30 lakh, Anjali Rs 50 lakh). At year end, the startup made Rs 80 lakh profit.

Step 1: Karan inputs the ratio 2:3:5 into the calculator. It returns simplified form (already simplest) and percentage shares: 20%, 30%, 50%.

Step 2: He applies the percentage to Rs 80 lakh profit: Karan's share = 20% of 80 = Rs 16 lakh, Vikram's = Rs 24 lakh, Anjali's = Rs 40 lakh. Sum = Rs 80 lakh, confirmed.

Step 3: For next year, Karan invests an extra Rs 30 lakh, making his investment Rs 50 lakh. New ratio: 50:30:50 = 5:3:5. New percentage shares: 38.5%, 23%, 38.5%.

Result: Karan's new share of Rs 1 crore projected profit next year jumps from Rs 20 lakh to Rs 38.5 lakh, a Rs 18.5 lakh increase, justifying the extra investment. He documents this revised partnership in the LLP agreement.

Frequently Asked Questions About Ratios

Indian students often ask how to simplify ratios with decimals, when to use direct versus inverse proportion, how partnership profit-sharing handles different investment durations, and the link between ratios and similar triangles in CBSE Class 10 geometry. The FAQ below addresses each with examples from NCERT, RS Aggarwal, and CAT prep textbooks.