Rates (Copy)
Practice Questions — 1.12 Rates
Question 1
A worker is paid Rs. 960 for 8 hours.
(a) Find their hourly rate of pay.
(b) How much will they earn in 35 hours?
Question 2
Exchange rate: 1 US dollar = Rs. 278.
(a) Convert Rs. 13 900 into US dollars.
(b) Convert 250 US dollars into rupees.
Question 3
A cyclist travels 45 km in 3 hours 45 minutes.
Find the average speed in km/h.
Question 4
A tap fills a tank at a rate of 12 litres per minute.
How long will it take to fill a tank of capacity 180 litres?
Question 5
A car travels 240 km using 20 litres of fuel.
(a) Find the fuel consumption in km per litre.
(b) How much fuel is needed to travel 480 km?
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 6
The pressure on a surface is 360 N/m² and the force is 180 N.
Find the area of the surface.
Question 7
The density of copper is 8.9 g/cm³.
Find the mass of a piece of copper of volume 120 cm³.
Question 8
The population of a town is 2.4 million and the area is 600 km².
Find the population density in people per km².
Question 9
A car travels 300 km in 4 hours 15 minutes.
Find its average speed in km/h.
Question 10
Water flows into a swimming pool at a rate of 1.5 m³ per minute.
How long will it take to fill 450 m³ of water?
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 11
The mass of a block of wood is 2.1 kg and its volume is 700 cm³.
Find the density of the block in g/cm³.
Question 12
A taxi charges a base fare of Rs. 300 plus Rs. 25 per kilometre.
If the fare for a journey is Rs. 650, how long was the journey in kilometres?
Question 13
A lorry travels 72 km at an average speed of 48 km/h.
How long does the journey take? Give your answer in hours and minutes.
Question 14
The pressure under a box is 250 N/m² when the box exerts a force of 500 N.
Find the base area of the box.
Question 15
The exchange rate is £1 = Rs. 360.
(a) Convert £250 into rupees.
(b) Convert Rs. 72 000 into pounds.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Answer key and explanations — 1.12 Rates
1.
(a) Hourly rate = 960 ÷ 8 = Rs. 120/hour
(b) 35 hours × 120 = Rs. 4200
Explanation: Rate = total ÷ time. Multiply by required time for extended pay.
2.
1 USD = Rs. 278
(a) Rs. 13 900 ÷ 278 = USD 50
(b) 250 × 278 = Rs. 69 500
Explanation: Conversions are direct proportion.
3.
Time = 3 h 45 min = 3.75 h
Speed = distance ÷ time = 45 ÷ 3.75 = 12 km/h
Explanation: Always convert mixed units to hours.
4.
Rate = 12 L/min, volume = 180 L
Time = 180 ÷ 12 = 15 minutes
5.
240 km ÷ 20 L = 12 km/L
(a) 12 km per litre
(b) 480 ÷ 12 = 40 L
Answer: 12 km/L and 40 L
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
6.
Pressure = Force ÷ Area → Area = Force ÷ Pressure
= 180 ÷ 360 = 0.5 m²
7.
Density = Mass ÷ Volume
= 8.9 g/cm³ × 120 cm³ = 1068 g = 1.068 kg
8.
Population density = 2 400 000 ÷ 600 = 4000 people/km²
9.
Time = 4 h 15 min = 4.25 h
Speed = 300 ÷ 4.25 ≈ 70.6 km/h
10.
Volume ÷ rate = 450 ÷ 1.5 = 300 minutes = 5 hours
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
11.
Mass = 2.1 kg = 2100 g
Density = 2100 ÷ 700 = 3 g/cm³
12.
Fare = 300 + 25x = 650
25x = 350 → x = 14 km
13.
Time = 72 ÷ 48 = 1.5 h = 1 h 30 min
14.
Area = Force ÷ Pressure = 500 ÷ 250 = 2 m²
15.
£1 = Rs. 360
(a) £250 = 250 × 360 = Rs. 90 000
(b) Rs. 72 000 ÷ 360 = £200
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course