Sec 1 Mathematics Ratio, Rate & Speed topical questions

Simplify each ratio.

1. (a)16 : 24[1]
2. (b)30 : 45 : 60[1]
3. (c)25 minutes : 1 hour[1]

A fruit seller packs 8 kg of oranges into bags of 1.6 kg each. How many bags does he get?

A cyclist rides 28 km in 2 hours at a steady speed. Find the distance covered in 5 hours at the same speed.

Express 45 minutes as a fraction of 2 hours, giving your answer in its simplest form.

Simplify each ratio.

1. (a)45 : 60[1]
2. (b)1.2 kg : 800 g[1]
3. (c)$2.40 : $3.60[1]

Share 88 marbles among Xiu, Yara and Zhi in the ratio 2 : 5 : 4.

A sum of $240 is shared among Ali, Ben and Cai in the ratio 3 : 4 : 5.

1. (a)Find the value of one part.[1]
2. (b)State each person’s share.[2]
3. (c)How much more does Cai receive than Ali?[1]

In a school hall, the ratio of teachers to students is 1 : 14. There are 495 people in the hall altogether.

1. (a)Find the number of students.[2]
2. (b)Another hall has the same teacher-to-student ratio and 6 teachers. How many students are there?[2]

A photocopier produces pages at a rate of 18 pages per minute.

1. (a)How long does it take to produce 225 pages? Give your answer in minutes and seconds.[2]
2. (b)How many pages can it produce in 7 minutes?[1]
3. (c)A faster copier produces 480 pages in 20 minutes. Which copier works at the higher rate?[1]

A hawker stall sells 3 plates of char kway teow for $12.90.

1. (a)Find the price of one plate.[1]
2. (b)Find the cost of 7 plates.[1]
3. (c)Mei pays $21.50 for some plates. How many plates does she buy?[2]

A cyclist rides 15 km to a park at 20 km/h, rests for 5 minutes, then rides 15 km home at 12 km/h.

1. (a)Find the time for the ride to the park, in minutes.[1]
2. (b)Find the time for the ride home, in minutes.[1]
3. (c)Find the total time for the whole outing, in hours and minutes.[1]
4. (d)Find the average speed for the whole outing.[2]

A van delivers parcels: 96 parcels in the morning taking 3 hours, then 64 parcels in the afternoon taking 2 hours.

1. (a)Find the van’s delivery rate for the whole day, in parcels per hour.[2]
2. (b)A driver claims the van delivered “at 32 parcels per hour in the morning, so the whole day was 32 parcels per hour”. Explain the error.[2]

A model train is built to a scale of 1 : 87. The real locomotive is 22 m long.

1. (a)Find the length of the model, in centimetres, correct to the nearest centimetre.[2]
2. (b)The model’s wheels are 2 cm in diameter. Find the real diameter, in metres.[2]

Two buses start at 08:00 from the same terminal. Bus A travels at 55 km/h and Bus B at 70 km/h, both towards the same city 420 km away.

1. (a)Find the journey time of each bus.[2]
2. (b)How far apart are the two buses at 11:00?[2]
3. (c)At what time does Bus B arrive?[1]

Aiden and Belle have stickers in the ratio 4 : 7. Belle gives 18 stickers to Aiden, after which they have equal numbers of stickers.

1. (a)Write expressions, in terms of x, for the numbers of stickers each has after the gift, if one part is x.[2]
2. (b)Form and solve an equation to find x.[2]
3. (c)State how many stickers each person had at first.[1]