Olympiad topic · P5–P6
Ratios
Ratio questions appear in the Hua Xia Cup's P4 to P6 first rounds, qualifying rounds and finals, such as linked ratios and ratios that change.
Try one
★★ MediumA community centre is packing a batch of gift bags for elderly residents.
The plan was for 6 volunteers to do it, taking 6 hours.
Every volunteer packs the same number of bags each hour.
On the day, only 4 volunteers came, and those 4 worked from start to finish.
How many hours longer than planned did the job take?
- Hint 1: If there were just one volunteer, how many hours would it take?
- Hint 2: The whole job is the same. How long would 4 take?
- 1.Call one volunteer's work in one hour 1 part. The plan was 6 people for 6 hours, so the whole job = 6 × 6 = 36 parts.
- 2.The job is still 36 parts. 4 people do 4 parts each hour, so they need 36 ÷ 4 = 9 hours.
- 3.9 − 6 = 3: 3 hours longer.
- ⚠️Common mistake: thinking 2 fewer people means 2 hours more. More people take less time: if the numbers of people are 6 : 4, the times are 4 : 6.
Answer: 3 hours
Four levels, step by step
- ★EasyFree2 question types · unlimited questionsSharing in a ratio.
- ★★MediumFree2 question types · unlimited questionsThree-way ratios, more workers fewer days.
- ★★★HardFree2 question types · unlimited questionsOne amount fixed while the ratio changes, speed and time.
- ★★★★Expert (competition level)VIP3 question types · unlimited questionsA ratio changing several times, distances in a race.
Ratios: what it is and how to solve it
Ratios compare two or more amounts; work out each amount from the parts.
For example: 91 chocolates shared 3 : 4 between a brother and sister. The sister's share? 3 + 4 = 7 parts, each 91 ÷ 7 = 13, so 13 × 4 = 52.
The key idea: Treat a ratio as parts: find one part, then multiply. When a ratio changes, hold on to the amount that didn't and make both ratios use the same parts for it. The usual method in Hong Kong primary schools seldom uses ratios; thinking in parts matches the secondary-school method.
Practise this topic free →Easy to Hard (★ to ★★★) all free, unlimited questions, no download