Rates, Ratios, and Proportions

Practice bank for UCAT Quantitative Reasoning questions involving rates (speed, cost per unit, flow rates), ratios, and direct/inverse proportion.

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Quick-Reference: Rates and Ratios

Speed, Distance, Time

Find	Formula
Speed	Distance / Time
Distance	Speed x Time
Time	Distance / Speed

Ratios

• A ratio compares two or more quantities: A : B
• To simplify, divide all parts by the highest common factor
• To share a total in a ratio A : B, each part = Total / (A + B) then multiply by A or B

Direct Proportion

If X doubles, Y doubles. Formula: Y = kX where k is constant.

Inverse Proportion

If X doubles, Y halves. Formula: Y = k/X where k is constant.

Unit Rates

Type	Example
Cost per item	Total cost / Number of items
Speed	Distance / Time
Flow rate	Volume / Time
Density	Mass / Volume

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Strategy