Sec 4 · G2 (N(A))

Problems in real-world contexts

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1. Taxation

Chargeable income	Rate	Tax
First $40,000	from the table	$ $550$
Next $16,400	$7\%$	$ $1148$
All $56,400		$ $1698$

Income tax: the first part from the table, then the band's rate on the rest

\displaystyle \text{table's tax} + \text{rate} \times \text{rest}

e.g.

\displaystyle 550 + \dfrac{7}{100} \times 16400

\displaystyle = 550 + 1148

\displaystyle = 1698

Chargeable income

\displaystyle \text{income} - \text{reliefs}

e.g.

\displaystyle 70200 - 23720

\displaystyle = 46480

GST in a price that includes 9% GST

\displaystyle \dfrac{9}{109} \times \text{price}

e.g.

\displaystyle \dfrac{9}{109} \times 1526

\displaystyle = 126

Restaurant bill: 10% service charge, then 9% GST on the total

\displaystyle \text{bill} \times 1.10 \times 1.09

e.g.

\displaystyle 80 \times 1.10 \times 1.09

\displaystyle = 95.92

Annual value (property tax) from a monthly rent

\displaystyle \text{monthly rent} \times 12

e.g.

\displaystyle 3400 \times 12

\displaystyle = 40800

📖 Worked example

Ali's chargeable income for the year is $61,200. The table shows the income tax rates. Calculate the income tax Ali pays for the year.

Chargeable income	Income tax rate (%)	Gross tax payable ($)
On the first $20,000	0	0
On the next $10,000	2	200
On the first $30,000		200
On the next $10,000	3.5	350
On the first $40,000		550
On the next $40,000	7	2,800
On the first $80,000		3,350
On the next $40,000	11.5	4,600
On the first $120,000		7,950
On the next $40,000	15	6,000
On the first $160,000		13,950

Step 1 of 3

From the table: the income tax on the first part of the chargeable income (in dollars)

\text{Tax on the first } 40000 \rightarrow 550

📖 Worked example

The annual value of a home is the rent it could earn in a year. Devi's family lives in a flat that could be rented out for $3,400 a month. The table shows the property tax rates for owner-occupied homes. Find the property tax payable for the year.

Annual value	Tax rate (%)	Property tax payable ($)
On the first $12,000	0	0
On the next $28,000	4	1,120
On the first $40,000		1,120
On the next $10,000	6	600
On the first $50,000		1,720
On the next $25,000	10	2,500
On the first $75,000		4,220
On the next $10,000	14	1,400
On the first $85,000		5,620
On the next $15,000	20	3,000
On the first $100,000		8,620

Step 1 of 4

Annual value = the rent for a year: 12 months (in dollars)

\text{Annual value} = 3400 \times 12

\phantom{\text{Annual value}} = 40800

📖 Worked example

The table shows the income tax rates. Chen Wei pays $2,437 in income tax for the year. Find Chen Wei's chargeable income.

Chargeable income	Income tax rate (%)	Gross tax payable ($)
On the first $20,000	0	0
On the next $15,000	2.5	375
On the first $35,000		375
On the next $15,000	5	750
On the first $50,000		1,125
On the next $30,000	8	2,400
On the first $80,000		3,525
On the next $40,000	12	4,800
On the first $120,000		8,325
On the next $40,000	15	6,000
On the first $160,000		14,325

Step 1 of 4

From the table: the largest 'first' amount whose tax is less than the tax paid (in dollars)

\text{Tax on the first } 50000 \rightarrow 1125

Practise this →

2. Time, timetables and time zones

12-hour	24-hour
12.15 a.m.	0015
7.45 a.m.	0745
12.05 p.m.	1205
7.45 p.m.	1945

The city is	Its time
ahead of Singapore	add the difference
behind Singapore	take away the difference
past 2400	the next day
before 0000	the day before

📖 Worked example

A coach leaves Singapore at 2050 and reaches Kuala Lumpur (in the same time zone) at 0240 the next day. Find the duration of the journey, in hours and minutes.

Step 1 of 2

From the start to midnight (2400)

24 \text{ h} - 20 \text{ h } 50 \text{ min} = 3 \text{ h } 10 \text{ min}

📖 Worked example

The table shows the time differences between Singapore and some cities. Kumar in Singapore plans to call a friend in Mumbai at 1415 on 14 May, Mumbai time. Find the time and date in Singapore when the call is made.

City	Time compared with Singapore
Mumbai	2 h 30 min behind Singapore
Seoul	1 h ahead of Singapore
Los Angeles	15 h behind Singapore

Step 1 of 3

From the table: how far ahead or behind Singapore

Mumbai is 2 h 30 min behind Singapore.

📖 Worked example

The table shows the time zones of some cities. A flight leaves Singapore at 0855 on 22 May, Singapore time. The flight takes 2 h 30 min. Find the local time and date when it lands in Bangkok.

City	Time zone
Singapore	UTC+8
London	UTC+1
Bangkok	UTC+7
Sydney	UTC+10

Step 1 of 5

Landing time in Singapore time: departure time + flight time

8 \text{ h } 55 \text{ min} + 2 \text{ h } 30 \text{ min}

= 10 \text{ h } 85 \text{ min}

= 11 \text{ h } 25 \text{ min} \quad (60 \text{ min} = 1 \text{ h})

Practise this →

3. Recipes and floor plans

Find	Round	e.g.
packs, boxes or tins to buy	UP	$2.4 \rightarrow 3$
servings you can make	DOWN	$26.7 \rightarrow 26$

A recipe for 4 servings, made for 6

\displaystyle \text{amount} \times \dfrac{\text{servings wanted}}{\text{servings in recipe}}

e.g.

\displaystyle 200 \times \dfrac{6}{4}

\displaystyle = 300

$200$ g of flour for 4 servings becomes $300$ g for 6

A plan at 1 : 50 (lengths times 50, areas times 50 squared)

\displaystyle \text{plan area} \times 50^{2}

e.g.

\displaystyle 32 \times 50^{2}

\displaystyle = 80000

$80\,000$ cm² is $8$ m² (1 m² is $10\,000$ cm²)

📖 Worked example

The table shows a recipe for chocolate cake for 8 servings, and how the ingredients are sold. Devi is making 30 servings and has to buy all the self-raising flour and cocoa powder. Find the least amount Devi pays for them.

Ingredient	For 8 servings	Sold in	Price
self-raising flour	240 g	500 g bag	$2.35
sugar	200 g	1 kg bag	$2.20
cocoa powder	60 g	200 g tin	$6.50
butter	160 g	250 g block	$4.95
eggs	4 eggs	tray of 10	$3.60

Step 1 of 3

Self-raising flour: the amount needed, then whole packs (pack size in g)

\dfrac{240}{8} \times 30 = 900 \text{ g}

\dfrac{900}{500} = 1.8 \rightarrow 2 \text{ packs}

2 \times 2.35 = 4.70

📖 Worked example

The diagram shows the floor plan of an L-shaped living and dining area. The floor is to be covered with vinyl flooring costing $42 per m². Find the cost of the flooring.

Step 1 of 3

The whole rectangle, then the corner cut out (in m²)

6.6 \times 4.8 = 31.68

2.4 \times 1.8 = 4.32

📖 Worked example

The diagram shows the floor plan of a flat, drawn to a scale of 1 : 40. The lengths marked are measured on the plan. Find the actual floor area of the bedroom, in m².

Step 1 of 3

Real lengths from the plan (in cm)

9 \times 40 = 360 \text{ cm}

13.5 \times 40 = 540 \text{ cm}

Practise this →

4. Real-world problems

Step	What to do
1	Each option's total, with every charge
2	Compare: choose the cheaper one
3	Answer: the choice AND its value

📖 Worked example

Ali needs a new phone and compares the two plans in the table. Ali uses about 45 GB of data a month. Over 24 months, which plan is cheaper? Find the total cost of the cheaper plan over the 24 months.

	Plan A (with phone)	Plan B (SIM only)
Monthly fee	$48	$15
Data each month	10 GB	15 GB
Extra data	$5 per GB	$6 per GB
Phone	$188 when you sign up	buy it yourself for $1,059

Step 1 of 5

Plan A: the cost each month (in dollars)

48 + (45 - 10) \times 5 = 223

📖 Worked example

85 students and 3 teachers go on an excursion to the zoo. They hire enough buses for everyone, and every student pays for an entrance ticket. The costs are shown in the table. The total cost is shared among the students only, and each student pays the same whole number of dollars, enough to cover the total cost. Find the least amount each student pays.

Hire of one bus	$495 (49 seats)
Entrance ticket	$8.50 per student (teachers free)

Step 1 of 4

Number of people

85 + 3 = 88

Practise this →

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Sec 4 · G2 (N(A))

Problems in real-world contexts

Practise problems in real-world contexts with step-by-step help. Free account.

Start free Worksheet (PDF)

1. Taxation

Chargeable income	Rate	Tax
First $40,000	from the table	$ $550$
Next $16,400	$7\%$	$ $1148$
All $56,400		$ $1698$

Income tax: the first part from the table, then the band's rate on the rest

\displaystyle \text{table's tax} + \text{rate} \times \text{rest}

e.g.

\displaystyle 550 + \dfrac{7}{100} \times 16400

\displaystyle = 550 + 1148

\displaystyle = 1698

Chargeable income

\displaystyle \text{income} - \text{reliefs}

e.g.

\displaystyle 70200 - 23720

\displaystyle = 46480

GST in a price that includes 9% GST

\displaystyle \dfrac{9}{109} \times \text{price}

e.g.

\displaystyle \dfrac{9}{109} \times 1526

\displaystyle = 126

Restaurant bill: 10% service charge, then 9% GST on the total

\displaystyle \text{bill} \times 1.10 \times 1.09

e.g.

\displaystyle 80 \times 1.10 \times 1.09

\displaystyle = 95.92

Annual value (property tax) from a monthly rent

\displaystyle \text{monthly rent} \times 12

e.g.

\displaystyle 3400 \times 12

\displaystyle = 40800

📖 Worked example

Ali's chargeable income for the year is $61,200. The table shows the income tax rates. Calculate the income tax Ali pays for the year.

Chargeable income	Income tax rate (%)	Gross tax payable ($)
On the first $20,000	0	0
On the next $10,000	2	200
On the first $30,000		200
On the next $10,000	3.5	350
On the first $40,000		550
On the next $40,000	7	2,800
On the first $80,000		3,350
On the next $40,000	11.5	4,600
On the first $120,000		7,950
On the next $40,000	15	6,000
On the first $160,000		13,950

Step 1 of 3

From the table: the income tax on the first part of the chargeable income (in dollars)

\text{Tax on the first } 40000 \rightarrow 550

📖 Worked example

Annual value	Tax rate (%)	Property tax payable ($)
On the first $12,000	0	0
On the next $28,000	4	1,120
On the first $40,000		1,120
On the next $10,000	6	600
On the first $50,000		1,720
On the next $25,000	10	2,500
On the first $75,000		4,220
On the next $10,000	14	1,400
On the first $85,000		5,620
On the next $15,000	20	3,000
On the first $100,000		8,620

Step 1 of 4

Annual value = the rent for a year: 12 months (in dollars)

\text{Annual value} = 3400 \times 12

\phantom{\text{Annual value}} = 40800

📖 Worked example

The table shows the income tax rates. Chen Wei pays $2,437 in income tax for the year. Find Chen Wei's chargeable income.

Chargeable income	Income tax rate (%)	Gross tax payable ($)
On the first $20,000	0	0
On the next $15,000	2.5	375
On the first $35,000		375
On the next $15,000	5	750
On the first $50,000		1,125
On the next $30,000	8	2,400
On the first $80,000		3,525
On the next $40,000	12	4,800
On the first $120,000		8,325
On the next $40,000	15	6,000
On the first $160,000		14,325

Step 1 of 4

From the table: the largest 'first' amount whose tax is less than the tax paid (in dollars)

\text{Tax on the first } 50000 \rightarrow 1125

Practise this →

2. Time, timetables and time zones

12-hour	24-hour
12.15 a.m.	0015
7.45 a.m.	0745
12.05 p.m.	1205
7.45 p.m.	1945

The city is	Its time
ahead of Singapore	add the difference
behind Singapore	take away the difference
past 2400	the next day
before 0000	the day before

📖 Worked example

A coach leaves Singapore at 2050 and reaches Kuala Lumpur (in the same time zone) at 0240 the next day. Find the duration of the journey, in hours and minutes.

Step 1 of 2

From the start to midnight (2400)

24 \text{ h} - 20 \text{ h } 50 \text{ min} = 3 \text{ h } 10 \text{ min}

📖 Worked example

City	Time compared with Singapore
Mumbai	2 h 30 min behind Singapore
Seoul	1 h ahead of Singapore
Los Angeles	15 h behind Singapore

Step 1 of 3

From the table: how far ahead or behind Singapore

Mumbai is 2 h 30 min behind Singapore.

📖 Worked example

The table shows the time zones of some cities. A flight leaves Singapore at 0855 on 22 May, Singapore time. The flight takes 2 h 30 min. Find the local time and date when it lands in Bangkok.

City	Time zone
Singapore	UTC+8
London	UTC+1
Bangkok	UTC+7
Sydney	UTC+10

Step 1 of 5

Landing time in Singapore time: departure time + flight time

8 \text{ h } 55 \text{ min} + 2 \text{ h } 30 \text{ min}

= 10 \text{ h } 85 \text{ min}

= 11 \text{ h } 25 \text{ min} \quad (60 \text{ min} = 1 \text{ h})

Practise this →

3. Recipes and floor plans

Find	Round	e.g.
packs, boxes or tins to buy	UP	$2.4 \rightarrow 3$
servings you can make	DOWN	$26.7 \rightarrow 26$

A recipe for 4 servings, made for 6

\displaystyle \text{amount} \times \dfrac{\text{servings wanted}}{\text{servings in recipe}}

e.g.

\displaystyle 200 \times \dfrac{6}{4}

\displaystyle = 300

$200$ g of flour for 4 servings becomes $300$ g for 6

A plan at 1 : 50 (lengths times 50, areas times 50 squared)

\displaystyle \text{plan area} \times 50^{2}

e.g.

\displaystyle 32 \times 50^{2}

\displaystyle = 80000

$80\,000$ cm² is $8$ m² (1 m² is $10\,000$ cm²)

📖 Worked example

Ingredient	For 8 servings	Sold in	Price
self-raising flour	240 g	500 g bag	$2.35
sugar	200 g	1 kg bag	$2.20
cocoa powder	60 g	200 g tin	$6.50
butter	160 g	250 g block	$4.95
eggs	4 eggs	tray of 10	$3.60

Step 1 of 3

Self-raising flour: the amount needed, then whole packs (pack size in g)

\dfrac{240}{8} \times 30 = 900 \text{ g}

\dfrac{900}{500} = 1.8 \rightarrow 2 \text{ packs}

2 \times 2.35 = 4.70

📖 Worked example

The diagram shows the floor plan of an L-shaped living and dining area. The floor is to be covered with vinyl flooring costing $42 per m². Find the cost of the flooring.

Step 1 of 3

The whole rectangle, then the corner cut out (in m²)

6.6 \times 4.8 = 31.68

2.4 \times 1.8 = 4.32

📖 Worked example

The diagram shows the floor plan of a flat, drawn to a scale of 1 : 40. The lengths marked are measured on the plan. Find the actual floor area of the bedroom, in m².

Step 1 of 3

Real lengths from the plan (in cm)

9 \times 40 = 360 \text{ cm}

13.5 \times 40 = 540 \text{ cm}

Practise this →

4. Real-world problems

Step	What to do
1	Each option's total, with every charge
2	Compare: choose the cheaper one
3	Answer: the choice AND its value

📖 Worked example

Ali needs a new phone and compares the two plans in the table. Ali uses about 45 GB of data a month. Over 24 months, which plan is cheaper? Find the total cost of the cheaper plan over the 24 months.

	Plan A (with phone)	Plan B (SIM only)
Monthly fee	$48	$15
Data each month	10 GB	15 GB
Extra data	$5 per GB	$6 per GB
Phone	$188 when you sign up	buy it yourself for $1,059

Step 1 of 5

Plan A: the cost each month (in dollars)

48 + (45 - 10) \times 5 = 223

📖 Worked example

Hire of one bus	$495 (49 seats)
Entrance ticket	$8.50 per student (teachers free)

Step 1 of 4

Number of people

85 + 3 = 88

Practise this →

Try a question: Problems in real-world contexts

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