Treat a ratio as a fixed multiple of a common unit — if two amounts are in ratio a:b, write them as ax and bx, then solve for x using whatever total or condition the question gives.
Ratios describe a relationship between quantities, not the quantities themselves — the trick to solving them is reintroducing a variable to represent the "unit" size.
Question: Two numbers are in the ratio 3:5. Their sum is 96. What are the two numbers?
Solution: Let the numbers be 3x and 5x. Then 3x + 5x = 96, so 8x = 96, giving x = 12. The numbers are 3×12 = 36 and 5×12 = 60.
Question: Divide ₹2,000 between two people in the ratio 2:3.
Solution: Total parts = 2 + 3 = 5. Each part = 2,000 ÷ 5 = 400. First share = 2 × 400 = ₹800. Second share = 3 × 400 = ₹1,200.
A proportion states that two ratios are equal, written a:b = c:d. Cross-multiplying (a × d = b × c) is the standard way to solve for an unknown value within a proportion.
Last reviewed: September 2026