GST and Service Charge

Percentages on a bill in Singapore: adding 9% GST to a price and taking it back out, a restaurant bill with a 10% service charge and GST, and a discount together with GST.

Before you start

To find a percentage of a quantity, write the percentage as a decimal and multiply: 9% of $80 is $0.09 \times 80 = 7.2$ , which is $7.20.

To increase a quantity by a percentage in one step, multiply it by 100% plus the increase; to decrease it, multiply by 100% minus the decrease. These are the multipliers: an increase of 9% is $\times 109\% = \times 1.09$ , and a decrease of 15% is $\times 85\% = \times 0.85$ . For one change after another, multiply the multipliers, in any order. To find an original value from a value after a change, divide by the multiplier.

In a shop, the marked price is the price on the tag before a discount, and the selling price is the price the buyer pays after it. "x% off" means that x% of the marked price is taken off, so the buyer pays $(100 - x)\%$ of it: "15% off" is $\times 0.85$ .

Money is given to the nearest cent. Keep the full calculator value in the working and round only the answer.

Goods and Services Tax (GST)

Goods and Services Tax (GST) is a tax on most goods and services bought in Singapore. A business registered for GST adds it to the price, collects it from the buyer and pays it to the government. The rate has changed: GST was 7% until 31 December 2022, 8% in 2023, and has been 9% since 1 January 2024. In this lesson GST is 9% unless a question gives another rate.

GST is a percentage of the price before GST. Adding 9% to a price is an increase of 9%, so the price with GST is 109% of the price before GST.

Rule: GST at 9%

$\text{GST} = 9\% \times \text{price before GST}$

$\text{Price with GST} = 109\% \times \text{price before GST} = \text{price before GST} \times 1.09$

Example 1: The price with GST

(a) The price of a printer before GST is $80. Find the GST and the price with GST.
(b) The price of a lamp before GST is $45.90. Find the price with GST.

Solution

(a) The price before GST is 100%. GST adds 9% of it, so the price with GST is 109% of the price before GST.

GST $= 9\% \times 80 = 0.09 \times 80 = 7.2$ , so the GST is $7.20.

Price with GST $= 80 + 7.20 = 87.20$ , so $87.20.

In one step: $80 \times 1.09 = 87.2$ , which is $87.20.

(b) Price with GST $= 45.90 \times 1.09 = 50.031$ , which is $50.03 to the nearest cent.

Check in two steps: GST $= 45.90 \times 0.09 = 4.131 \approx 4.13$ , and $45.90 + 4.13 = 50.03$ .

(a) The GST is $7.20 and the price with GST is $87.20.
(b) The price with GST is $50.03.

How prices are shown

A business in Singapore that is registered for GST must show its prices with GST included, so the price on a tag at a mall is the price paid at the counter: the shop has already worked out price before GST $\times 1.09$ . A price before GST is the price a business works with before it adds the tax (for example on a supplier’s quotation, or in the shop’s own sums). In the questions of this lesson, a price "before GST" means that price.

Hotels and restaurants that add a service charge may instead show their prices before the service charge and GST, with a clear notice that both will be added. Such prices are often written with "++" after them, as in $18++. The bill then adds both.

Not every seller charges GST: only a business registered for GST does, so a small stall may charge no GST at all.

Finding the Price Before GST

Sometimes the price with GST is known and the price before GST is wanted, for example to find how much of a price on a tag is GST. This is a reverse percentage: the price with GST is 109% of the price before GST, so divide the price with GST by 1.09, or find 1% and then 100%. The 9% is a percentage of the price before GST, so it is never taken of the price with GST.

Rule: taking GST out of a price

$\text{Price before GST} = \text{price with GST} \div 1.09$

$\text{GST} = \text{price with GST} - \text{price before GST}$

Example 2: From the price with GST to the price before GST

(a) The bill for repairing a washing machine is $87.20, including GST. Find the price before GST and the GST.
(b) A rice cooker costs $49.90 at a shop in a mall. The price includes GST. How much of the $49.90 is GST?

Solution

(a) The price with GST is 109% of the price before GST, so 109% is $87.20.

Unitary method. 1% is $87.20 \div 109 = 0.80$ , so 100% is $0.80 \times 100 = 80$ .

By the multiplier. Price before GST $= 87.20 \div 1.09 = 80$ , so $80.

GST $= 87.20 - 80 = 7.20$ , so $7.20.

Check by working forward: $80 \times 1.09 = 87.20$ .

(b) Price before GST $= 49.90 \div 1.09 = 45.7798\ldots$

GST $= 49.90 - 45.7798\ldots = 4.1201\ldots \approx 4.12$ , so $4.12. The full value $45.7798\ldots$ is kept in the working and only the answer is rounded.

Check: $45.78 \times 1.09 = 49.9002$ , which is $49.90 to the nearest cent.

(a) The price before GST is $80 and the GST is $7.20.
(b) $4.12 of the price is GST.

Service Charge and GST on a Restaurant Bill

Many restaurants in Singapore add a service charge, commonly 10% of the price of the food and drinks. GST is a tax on goods and services, and the service charge is part of the price the restaurant charges for what it supplies, so GST is charged on the service charge too. The GST on the bill is 9% of the food, the drinks and the service charge together.

On a meal of $100, the service charge is 10% of $100, which is $10, and the subtotal is $110. The GST is 9% of $110, which is $9.90, not 9% of $100. The bill is $119.90. The 90 cents more than $119 is the GST on the $10 service charge.

Rule: a restaurant bill

$\text{Service charge} = 10\% \times \text{price of the food and drinks}$

$\text{GST} = 9\% \times (\text{food and drinks} + \text{service charge})$

$\text{Bill} = \text{food and drinks} \times 1.10 \times 1.09 = \text{food and drinks} \times 1.199$

What the order of the steps changes, and what it does not

Each percentage is taken of a different amount. The service charge is 10% of the food and drinks; the GST is 9% of the food, drinks and service charge together. So the service charge is worked out first: the GST cannot be found until the service charge is known, because GST is charged on it. Adding the two rates, $10\% + 9\% = 19\%$ , leaves out the GST on the service charge.

In one step: the subtotal is 110% of the food and drinks, so multiply by 1.10; the bill is 109% of the subtotal, so multiply by 1.09. The bill is $1.10 \times 1.09 = 1.199$ times the price of the food and drinks, which is 119.9% of it.

Two multipliers give the same product in either order ( $1.09 \times 1.10 = 1.199$ too), so the total is 119.9% of the food and drinks in either order. What the order of the steps decides is the split: the two amounts printed on the bill. On the $100 meal, the service charge is $10 and the GST is $9.90. Adding GST first and then taking 10% of the price with GST would give the same total, $119.90, but split as a service charge of $10.90 and GST of $9: a service charge on the tax. In this lesson, as on a usual restaurant bill, the service charge is taken of the food and drinks only, and the GST is added after it.

Example 3: A restaurant bill

Hui Min's family has dinner at a restaurant. The food and drinks come to $86.40. The restaurant adds a 10% service charge, and then 9% GST. Find the service charge, the GST and the total bill.

Solution

The service charge is a percentage of the food and drinks. The GST is a percentage of the subtotal, which is the food and drinks with the service charge added.

Service charge $= 10\% \times 86.40 = 8.64$ , so $8.64.

Subtotal $= 86.40 + 8.64 = 95.04$ , so $95.04. This is 110% of the food and drinks.

GST $= 9\% \times 95.04 = 8.5536 \approx 8.55$ , so $8.55.

Total bill $= 95.04 + 8.5536 = 103.5936 \approx 103.59$ , so $103.59.

In one step: $86.40 \times 1.10 \times 1.09 = 86.40 \times 1.199 = 103.5936$ , which is $103.59, the same.

The service charge is $8.64, the GST is $8.55 and the total bill is $103.59.

Discount and GST Together

When a price before GST is discounted, the GST is charged on the price after the discount. In one step, multiply by the multiplier of the discount and by 1.09. The two multipliers can be multiplied in either order, so taking off the discount first or adding GST first gives the same price. That is why a discount on a tag price that already includes GST works out the same: 15% off the price with GST is the same as 15% off the price before GST, with GST then added.

Example 4: A discount, then GST

A printer costs $240 before GST, and there is a 15% discount on it. GST of 9% is charged on the price after the discount. Find
(a) the price paid for the printer,
(b) the GST paid.
(c) Show that adding GST first and then taking 15% off gives the same price.

Solution

(a) Price after the discount $= 240 \times 0.85 = 204$ , so $204.

Price with GST $= 204 \times 1.09 = 222.36$ , so $222.36.

In one line: $240 \times 0.85 \times 1.09 = 222.36$

(b) GST $= 9\% \times 204 = 18.36$ , so $18.36. Check: $204 + 18.36 = 222.36$ .

(c) GST first: $240 \times 1.09 = 261.60$ . Then 15% off: $261.60 \times 0.85 = 222.36$ . The price is the same, because $0.85 \times 1.09 = 1.09 \times 0.85$ .

(a) The price paid is $222.36.
(b) The GST paid is $18.36.
(c) Both orders give $222.36.

Example 5: A discount, a service charge and GST

The prices on a restaurant's menu are marked "++": a service charge and GST are added to them. Mr Tan's family orders food and drinks that come to $120 on the menu. As a member, Mr Tan gets 15% off the food and drinks. The restaurant takes off the discount, then adds a 10% service charge, then 9% GST. Find the total bill.

Solution

Price after the discount $= 120 \times 0.85 = 102$ , so $102.

Service charge $= 10\% \times 102 = 10.20$ , so the subtotal is $102 + 10.20 = 112.20$ , which is $112.20.

GST $= 9\% \times 112.20 = 10.098$

Total bill $= 112.20 + 10.098 = 122.298 \approx 122.30$

In one line: $120 \times 0.85 \times 1.10 \times 1.09 = 122.298$ , which is $122.30.

The total bill is $122.30.

Common Mistakes

Taking 9% off a price with GST to remove the GST. For a bill of $87.20 including GST, $87.20 - 9\% \times 87.20 = 79.352$ gives $79.35, which is wrong: $79.35 \times 1.09 \approx 86.49$ , not 87.20. The 9% is of the price before GST, so divide: $87.20 \div 1.09 = 80$ .
Adding GST to a price that already includes it. A rice cooker tagged $49.90 at a shop that charges GST costs $49.90 at the counter. Working out $49.90 \times 1.09 = 54.391$ , about $54.39, counts the GST twice.
Adding 10% and 9% on a restaurant bill. Multiplying by 1.19 leaves out the GST on the service charge. On food and drinks of $86.40, $86.40 \times 1.19 = 102.816$ gives $102.82, but the bill is $86.40 \times 1.199 = 103.5936$ , which is $103.59.
Taking GST of the price before a discount. With 15% off a printer at $240 before GST, the GST is 9% of $204, the price after the discount, which is $18.36, not 9% of $240, which is $21.60.

Practice

Try each question before you open its solution. GST is 9% and a service charge is 10% unless the question says otherwise. Give money to the nearest cent.

Question 1

A storybook costs $12.80 before GST. Find the GST and the price with GST.

ShowHide solution

GST $= 9\% \times 12.80 = 0.09 \times 12.80 = 1.152 \approx 1.15$ , so $1.15.

Price with GST $= 12.80 \times 1.09 = 13.952 \approx 13.95$ , so $13.95.

Check: $12.80 + 1.15 = 13.95$

The GST is $1.15 and the price with GST is $13.95.

Question 2

The price of a backpack before GST is $56. Find the GST and the price with GST.

ShowHide solution

GST $= 9\% \times 56 = 0.09 \times 56 = 5.04$ , so $5.04.

Price with GST $= 56 + 5.04 = 61.04$

Check in one step: $56 \times 1.09 = 61.04$

The GST is $5.04 and the price with GST is $61.04.

Question 3

Each of these prices includes 9% GST. Find the price before GST and the GST in it.
(a) A pair of headphones at $130.80
(b) A book at $35.90

ShowHide solution

(a) The price with GST is 109% of the price before GST, so 109% is $130.80.

1% is $130.80 \div 109 = 1.20$ , so 100% is $1.20 \times 100 = 120$ . (Or: $130.80 \div 1.09 = 120$ .)

GST $= 130.80 - 120 = 10.80$ . Check: $120 \times 1.09 = 130.80$ .

(b) Price before GST $= 35.90 \div 1.09 = 32.9357\ldots \approx 32.94$

GST $= 35.90 - 32.9357\ldots = 2.9642\ldots \approx 2.96$

Check: $32.94 \times 1.09 = 35.9046$ , which is $35.90 to the nearest cent.

(a) The price before GST is $120 and the GST is $10.80.
(b) The price before GST is $32.94 and the GST is $2.96.

Question 4

A café lists a set lunch at $18++: a 10% service charge and then 9% GST are added to the $18. Find the service charge, the GST and the amount paid for the set lunch.

ShowHide solution

Service charge $= 10\% \times 18 = 1.80$ , so $1.80. Subtotal $= 18 + 1.80 = 19.80$ .

GST $= 9\% \times 19.80 = 1.782 \approx 1.78$ , so $1.78.

Amount paid $= 19.80 + 1.782 = 21.582 \approx 21.58$ . In one step: $18 \times 1.199 = 21.582$ .

Check: $18 + 1.80 + 1.78 = 21.58$

The service charge is $1.80, the GST is $1.78 and the amount paid is $21.58.

Question 5

Siti's family has lunch at a restaurant. The food and drinks come to $68.50. The restaurant adds a 10% service charge, and then 9% GST.
(a) Find the service charge, the GST and the total bill.
(b) Siti works out the bill as $68.50 \times 1.19$ . Explain why this is wrong, and find, without rounding, the difference between her value and the true bill.

ShowHide solution

(a) Service charge $= 10\% \times 68.50 = 6.85$ , so $6.85.

Subtotal $= 68.50 + 6.85 = 75.35$

GST $= 9\% \times 75.35 = 6.7815 \approx 6.78$ , so $6.78.

Total bill $= 75.35 + 6.7815 = 82.1315 \approx 82.13$ . In one step: $68.50 \times 1.199 = 82.1315$ .

(b) Multiplying by 1.19 adds 10% and 9% of the food and drinks, but GST is charged on the service charge too. $68.50 \times 1.19 = 81.515$ , which is $82.1315 - 81.515 = 0.6165$ less than the true bill.

That difference is exactly the GST on the service charge: $9\% \times 6.85 = 0.6165$ .

(a) The service charge is $6.85, the GST is $6.78 and the total bill is $82.13.
(b) 1.19 leaves out the GST on the service charge. Without rounding, her value is $0.6165 less than the true bill: exactly the GST on the service charge. (Each bill rounded to the nearest cent, $81.52 against $82.13, differs by 61 cents.)

Question 6

A receipt from 2023, when GST was 8%, shows that Mrs Goh paid $54 for a toaster, including GST.
(a) Find the price of the toaster before GST, and the GST she paid.
(b) With the same price before GST, what would the toaster cost with GST at 9%?

ShowHide solution

(a) In 2023 the price with GST was 108% of the price before GST. 1% is $54 \div 108 = 0.5$ , so 100% is $0.5 \times 100 = 50$ , which is $50. (Or: $54 \div 1.08 = 50$ .)

GST $= 54 - 50 = 4$ , so $4. Check: $50 \times 1.08 = 54$ .

(b) $50 \times 1.09 = 54.5$ , so $54.50, which is 50 cents more.

(a) The price before GST was $50 and the GST was $4.
(b) It would cost $54.50.

Question 7

The price of a laptop before GST was $1500 in 2022, in 2023 and in 2024. GST was 7% in 2022, 8% in 2023 and 9% in 2024.
(a) Find the price with GST in each year.
(b) By what percentage did the price with GST rise from 2022 to 2024? Give your answer correct to 3 significant figures.

ShowHide solution

(a) 2022: $1500 \times 1.07 = 1605$ . 2023: $1500 \times 1.08 = 1620$ . 2024: $1500 \times 1.09 = 1635$ .

(b) The rise is $1635 - 1605 = 30$ , so $30.

As a percentage of the 2022 price with GST: $\frac{30}{1605} \times 100\% = 1.869\ldots\% \approx 1.87\%$

The rate of GST rose by 2 percentage points, but the price with GST rose by only about 1.87%, because the $30 is compared with the whole 2022 price with GST, $1605.

(a) The price with GST was $1605 in 2022, $1620 in 2023 and $1635 in 2024.
(b) It rose by about 1.87%.

Question 8

At a restaurant, the food and drinks for Ali's family come to $40. A 10% service charge and 9% GST are added.
(a) Find the service charge, the GST and the total bill when the service charge is worked out first.
(b) Ali says, "If the GST were worked out first and the 10% then taken of the price with GST, the bill would be bigger." Work the bill out that way, and say whether he is right.

ShowHide solution

(a) Service charge $= 10\% \times 40 = 4$ , so $4. Subtotal $= 40 + 4 = 44$ .

GST $= 9\% \times 44 = 3.96$ , so $3.96. Total $= 44 + 3.96 = 47.96$ , which is $47.96.

(b) GST first: $9\% \times 40 = 3.60$ , so $3.60, and $40 + 3.60 = 43.60$ . Then 10% of $43.60 is $4.36, and $43.60 + 4.36 = 47.96$ .

The total is the same, $47.96, because $40 \times 1.10 \times 1.09 = 40 \times 1.09 \times 1.10$ . Only the split differs: $4 and $3.96 in (a), $4.36 and $3.60 in (b).

(a) The service charge is $4, the GST is $3.96 and the total bill is $47.96.
(b) Ali is not right: the total is $47.96 either way; only the service charge and the GST printed on the bill change.

Question 9

Mr Tan's bill at a restaurant is $59.95. It includes a 10% service charge on the food and drinks and 9% GST on the food, drinks and service charge. Find the price of the food and drinks, the service charge and the GST.

ShowHide solution

The bill is 109% of the subtotal, so the subtotal is $59.95 \div 1.09 = 55$ , which is $55.

The subtotal is 110% of the food and drinks, so the food and drinks are $55 \div 1.10 = 50$ , which is $50.

In one step: $59.95 \div 1.199 = 50$ .

Service charge $= 10\% \times 50 = 5$ , so $5. GST $= 9\% \times 55 = 4.95$ , so $4.95.

Check: $50 + 5 + 4.95 = 59.95$

The food and drinks cost $50, the service charge is $5 and the GST is $4.95.

Question 10

A supplier sells projectors to schools at $680 each before GST, with a 12% discount for schools. GST is charged on the price after the discount. Find
(a) the price a school pays for one projector,
(b) the GST in that price.

ShowHide solution

(a) Price after the discount $= 680 \times 0.88 = 598.40$ , so $598.40.

Price with GST $= 598.40 \times 1.09 = 652.256 \approx 652.26$

(b) GST $= 9\% \times 598.40 = 53.856 \approx 53.86$

Check: $598.40 + 53.86 = 652.26$

(a) A school pays $652.26.
(b) The GST is $53.86.

Question 11

At a restaurant whose menu prices are marked "++", the food and drinks for a family come to $148. Members get 20% off the food and drinks. The discount is taken off first, and then a 10% service charge and 9% GST are added.
(a) Find the total bill for a member, and for someone who is not a member.
(b) How much does a member save?
(c) Ali says that a member saves 20% of $148, which is $29.60. Explain why the saving is more than this.

ShowHide solution

(a) Not a member: $148 \times 1.10 \times 1.09 = 148 \times 1.199 = 177.452 \approx 177.45$

Member: $148 \times 0.8 = 118.40$ , and $118.40 \times 1.199 = 141.9616 \approx 141.96$

(b) Saving $= 177.452 - 141.9616 = 35.4904 \approx 35.49$

(c) The member's bill is $148 \times 0.8 \times 1.199$ and the other bill is $148 \times 1.199$ , so the member pays 80% of the whole bill and saves 20% of it: $20\% \times 177.452 = 35.4904$ .

In other words, the member saves the $29.60 taken off the food and drinks and the service charge and GST that would have been charged on that $29.60: $29.60 \times 0.199 = 5.8904$ , and $29.60 + 5.8904 = 35.4904$ .

(a) A member pays $141.96; someone who is not a member pays $177.45.
(b) A member saves $35.49.
(c) The discount is taken before the service charge and GST, so the member also saves the service charge and GST on the $29.60: the saving is 20% of the whole bill.

Key Points

GST in Singapore has been 9% since 1 January 2024 (8% in 2023, 7% until 31 December 2022). Price with GST = price before GST × 1.09.
A business registered for GST must show its prices with GST included. To find the price before GST, divide by 1.09; never take 9% of the price with GST.
Hotels and restaurants that add a service charge may show prices before the service charge and GST, with a clear notice that both will be added; such prices are often written with "++".
A restaurant bill: the service charge is 10% of the food and drinks, and GST is 9% of the food, drinks and service charge together. Bill = food and drinks × 1.10 × 1.09 = food and drinks × 1.199, not × 1.19.
The total is the same in either order; the order decides how it is split between service charge and GST.
With a discount and GST, GST is charged on the price after the discount. Multipliers give the same product in either order.
Give money to the nearest cent, and round only at the end.