A ratio compares quantities in a fixed relationship. Many reasoning questions become simpler when you convert the ratio into equal-sized parts before calculating the actual amounts.
Divide a total into parts
Red and blue counters are in the ratio 2:3, with 35 counters altogether. The ratio has five total parts. One part is 35 ÷ 5 = 7 counters.
Red therefore has 2 × 7 = 14, and blue has 3 × 7 = 21. Check that 14 + 21 = 35 and that 14:21 simplifies to 2:3.
Part-to-part is not part-to-whole
The ratio of red to blue is 2:3. The fraction of all counters that are red is 2/5, not 2/3. The denominator changes because the comparison changed from blue counters to all counters.
This distinction matters whenever a question switches between a ratio, a fraction and a percentage. Identify the comparison quantity before calculating.
Scale both sides together
If a recipe uses three cups of ingredient A for every two cups of B, doubling the recipe requires six and four. Adding the same amount to both sides does not generally preserve a ratio: four to three is different from three to two.
Proportional scaling multiplies both quantities by the same factor.
Try a difference question
Two groups are in the ratio 5:2, and the larger group has 18 more members. The difference is three ratio parts, so one part is 18 ÷ 3 = 6. The groups contain 30 and 12 members.
Here the given 18 is the difference, not the total. Dividing it by seven would answer the wrong question.
Final checks
Ask whether the supplied amount is a total, a difference or one share. Then verify both the requested relationship and the arithmetic. A good ratio solution should satisfy all the original quantities, not merely produce numbers that look proportionate.