Ratio, Proportion & Partnership

Ratio, Proportion & Partnership

Concept

A ratio is a comparison of two quantities — it tells you how many times one quantity is of another. A proportion states that two ratios are equal. The most practical use in SSC is dividing things in given ratios and scaling recipes, mixtures, or profit shares. When you have a ratio a:b and the total is known, each share = (a/(a+b)) × total.

Direct Proportion: More of A means more of B (double the recipe, double the ingredients). Inverse Proportion: More of A means less of B (more workers, less time to complete a job).

Partnership is the most common application. Partners contribute capital for different time periods. Their profit/loss sharing ratio = (Capital₁ × Time₁) : (Capital₂ × Time₂) : … This is called the “time-weighted capital” method. If a partner adds or withdraws money mid-period, calculate each period separately.

Key Points

• If a:b = c:d, then a/b = c/d and ad = bc. This is the “cross-multiply” rule.
• To divide quantity Q in ratio a:b:c: each share = Q × (individual sum) / (total sum of ratios).
• If A:B = 2:3 and B:C = 4:5, combine by making B equal: A:B:C = 8:12:15 (LCM of B denominators 3 and 4 is 12, so 2×4:3×4:3×5 = 8:12:15).
• Partnership: Active partners (who work) may get salary + profit share — treat salary as separate from profit distribution.
• If investments are for different time periods, reduce each to a “unit time equivalent” before taking ratios.

Worked Example

Q: A and B invest ₹3,000 and ₹5,000 respectively in a business. After 8 months, A adds ₹2,000 more and B withdraws ₹1,000. If the profit after a year is ₹22,000, find A’s share. Approach: A: 3000 × 8 + 5000 × 4 = 24000 + 20000 = 44000. B: 5000 × 8 + 4000 × 4 = 40000 + 16000 = 56000. Ratio = 44000:56000 = 11:14. A’s share = 11/(11+14) × 22000 = 11/25 × 22000 = ₹9,680. Answer: ₹9,680

SSC Pattern / Tips

• Always break the time period when capital changes mid-period — calculate each segment separately.
• In ratio problems, if combining two ratios where one term is common, use LCM method to harmonise.
• For three-component ratio, the sum of individual terms = (total / sum of ratio terms) × individual ratio term.