A Math

A Math (IGCSE)

E Math

H1 Math

H2 Math

IB HL Math

IB SL Math

IP Math

<p>A clothing store purchases $600$
 shirts at a wholesale price of $\$12$
 each. If <strong>5%</strong>
 of the shirts are damaged and need to be sold at a <strong>20%</strong>
 discount, and the store aims to achieve a <strong>25%</strong>
 profit on the cost price, what should be the selling price of the undamaged shirts?</p>

A clothing store purchases $600$
 shirts at a wholesale price of $\$12$
 each. If **5%**
 of the shirts are damaged and need to be sold at a **20%**
 discount, and the store aims to achieve a **25%**
 profit on the cost price, what should be the selling price of the undamaged shirts?

Percentages involving Finances: Profit and Loss

Percentages involving Finances: Discount

 Percentages involving Finances: Profit, Discount

Percentages

<p>A tech store is selling a laptop at $\$1200$ after offering a discount of $25$<strong>%</strong>. Despite the discount, the store still earns a profit of <strong>20%</strong>.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find the original price of the laptop before the discount.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the cost price of the laptop.</span></div></li></ol>

A tech store is selling a laptop at $\$1200$ after offering a discount of $25$**%**. Despite the discount, the store still earns a profit of **20%**.

Find the original price of the laptop before the discount.

<p>A farmer has $3200$ watermelons to be sold at $\$4.50$ each. If $5\%$ of the watermelons were found to be overripe and unsellable, and the farmer managed to make a $30\%$ profit in total, find the cost price per watermelon.</p>

A farmer has $3200$ watermelons to be sold at $\$4.50$ each. If $5\%$ of the watermelons were found to be overripe and unsellable, and the farmer managed to make a $30\%$ profit in total, find the cost price per watermelon.

<p>Phoebe has $20$ orange-flavour candies, which is $80\%$ of the total number of candies she has, and the rest are peach-flavour candies. Rachel has in total $50$ candies, of which $30\%$ are orange-flavour candies and the rest are peach-flavour candies. Rachel gives some of her candies to Phoebe such that Rachel has now $40\%$ of orange-flavour candies and Phoebe has now $50\%$ of orange-flavour candies. Find</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the number of peach-flavour candies Phoebe originally has,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the number of orange-flavour and peach-flavour candies Rachel originally has,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the number of candies that Rachel gives to Phoebe.</span></div></li></ol>

Phoebe has $20$ orange-flavour candies, which is $80\%$ of the total number of candies she has, and the rest are peach-flavour candies. Rachel has in total $50$ candies, of which $30\%$ are orange-flavour candies and the rest are peach-flavour candies. Rachel gives some of her candies to Phoebe such that Rachel has now $40\%$ of orange-flavour candies and Phoebe has now $50\%$ of orange-flavour candies. Find

the number of peach-flavour candies Phoebe originally has,

the number of orange-flavour and peach-flavour candies Rachel originally has,

the number of candies that Rachel gives to Phoebe.

Basics of Percentage

<p>Leonard is planning to buy a new cooker and he noticed there are three different shops selling the same brand of cooker. The sales plans of the three shops are as follows (GST rate is $9\%$):</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767616655834-q6r3h265gs.png?token=eyJraWQiOiJzdG9yYWdlLXVybC1zaWduaW5nLWtleV9iZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MTY2NTU4MzQtcTZyM2gyNjVncy5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzg1NzEzMjU3LCJleHAiOjE3ODU3MTM1NTd9.sLLUDxRFi6Tha4FdPtktiCYaJBaF82V_xksFlzYHQII" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">For each of the three shops, find the price Leonard needs to pay if he wants to buy only one such cooker. Hence, state which shop should Leonard choose.</span></div></li><li><div class="list-item-content"><span class="list-item-text">One of Leonard's friends, Vincent, also wants to buy a such cooker, and Vincent agrees to share the bill equally with Leonard if possible. State which shop should they choose by providing detailed workings.</span></div></li></ol>

Leonard is planning to buy a new cooker and he noticed there are three different shops selling the same brand of cooker. The sales plans of the three shops are as follows (GST rate is $9\%$):

For each of the three shops, find the price Leonard needs to pay if he wants to buy only one such cooker. Hence, state which shop should Leonard choose.

One of Leonard's friends, Vincent, also wants to buy a such cooker, and Vincent agrees to share the bill equally with Leonard if possible. State which shop should they choose by providing detailed workings.

Percentages involving Finances: GST

Percentage Change and Reverse Percentage

Percentages involving Finances: Discount and GST

<p>Jimmy and Richard have lunch together at a restaurant. The receipt is as follows:</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767616429274-a5u4aytotxh.png?token=eyJraWQiOiJzdG9yYWdlLXVybC1zaWduaW5nLWtleV9iZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MTY0MjkyNzQtYTV1NGF5dG90eGgucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc4NTcxMzI1NywiZXhwIjoxNzg1NzEzNTU3fQ.VoCm0RbANATOGlRCVFM6kncTWqFI33f-COyVnv8PDwc" style="max-width: min(280px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="i-list"><li><div class="list-item-paragraph">Complete the receipt by finding the following:</div><ol class="abc-list"><li><div class="list-item-paragraph">the discount in percentage,</div></li><li><div class="list-item-paragraph">the service charge amount,</div></li><li><div class="list-item-paragraph">the GST amount (Round to the nearest cent),</div></li><li><div class="list-item-paragraph">the total price of this meal.</div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">Jimmy argues that it would be cheaper in total if the service charge and GST are included before discount. Do you agree with Jimmy? State your reasons by providing detailed workings.</span></div></li></ol>

Jimmy and Richard have lunch together at a restaurant. The receipt is as follows:

Complete the receipt by finding the following: (a) the discount in percentage, (b) the service charge amount, (c) the GST amount (Round to the nearest cent), (d) the total price of this meal.

Jimmy argues that it would be cheaper in total if the service charge and GST are included before discount. Do you agree with Jimmy? State your reasons by providing detailed workings.

<p>On $15$ December $2022$, Jia Yi bought a personal computer at a shopping mall at a price of $\$1,605$, inclusive of GST (Goods and Services Tax) of $7\%$.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the price of the personal computer before GST.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the amount of GST that Jia Yi paid for the personal computer.</span></div></li></ol>
<p>The shopping mall will offer a discount of $12\%$ on the personal computer during Christmas & New Year's Holiday from $24$ December $2022$ to $3$ January $2023$. And from $1$ January $2023$, the GST in Singapore will be increased by one percentage point from $7\%$.</p>
<ol class="i-list" start="3"><li><div class="list-item-content"><span class="list-item-text">Find the new GST rate from $1$ January $2023$.</span></div></li><li><div class="list-item-paragraph">Find the price of the personal computer (including GST), respectively, if Jia Yi buys it on</div><ol class="abc-list"><li><div class="list-item-paragraph">$26$ December $2022$,</div></li><li><div class="list-item-paragraph">$2$ January $2023$,</div></li><li><div class="list-item-paragraph">$4$ January $2023$, </div></li></ol><div class="list-item-after-content">assuming the price of the personal computer before GST does not change.</div></li></ol>

On $15$ December $2022$, Jia Yi bought a personal computer at a shopping mall at a price of $\$1,605$, inclusive of GST (Goods and Services Tax) of $7\%$.

Find the price of the personal computer before GST.

Find the amount of GST that Jia Yi paid for the personal computer.

The shopping mall will offer a discount of $12\%$ on the personal computer during Christmas & New Year's Holiday from $24$ December $2022$ to $3$ January $2023$. And from $1$ January $2023$, the GST in Singapore will be increased by one percentage point from $7\%$.

Find the new GST rate from $1$ January $2023$.

Find the price of the personal computer (including GST), respectively, if Jia Yi buys it on (a) $26$ December $2022$, (b) $2$ January $2023$, (c) $4$ January $2023$, assuming the price of the personal computer before GST does not change.

<p>A cake shop sells cupcakes and profits at a percentage of $80\%$ on the cost of raw materials. The cost of raw materials then decreases by $20\%$, thus the cake shop offers a discount of cupcake at $10\%$ for $10$ days. Then the cake shop retrieves the marked selling price while the cost of raw materials does not change.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the percentage profit of the cake shop during the discounting period.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the percentage profit of the cake shop after the discounting period.</span></div></li><li><div class="list-item-paragraph">The marked selling price of each cupcake is $\$18$. The cake shop sells $120$ cupcakes on average every day during the $10$ days of discount. After retrieving the marked selling price, the cake shop sells $85$ cupcakes on average every day for another $10$ days.</div><div class="list-item-paragraph">Find the total amount of profit of this cake shop during the $20$ days, considering only raw materials as the cost.

</div></li></ol>

A cake shop sells cupcakes and profits at a percentage of $80\%$ on the cost of raw materials. The cost of raw materials then decreases by $20\%$, thus the cake shop offers a discount of cupcake at $10\%$ for $10$ days. Then the cake shop retrieves the marked selling price while the cost of raw materials does not change.

Find the percentage profit of the cake shop during the discounting period.

Find the percentage profit of the cake shop after the discounting period.

Percentages involving Finances: Profit, Loss, and Discount

<p>A book at bookstore A is marked at $\$30$ but sold at $\$24$. Another bookstore B sells this kind of book at $\$28$ after a percentage discount of $30\%$. And bookstore B offers a further percentage discount of $20\%$ on the part of purchasing beyond $100$ if customers purchase more than $100$ books of this kind.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the percentage discounts of the book at bookstore A.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the marked price of the book at bookstore B.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the selling price and the overall percentage discount of the book at bookstore B for the part of purchasing beyond $100$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">A school is planning to buy this kind of book for the students. Find which bookstore, A or B, has a cheaper total price if the school wants to buy $400$ such books.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the minimum number of books one will find it cheaper to buy from bookstore B than bookstore A.</span></div></li></ol>

A book at bookstore A is marked at $\$30$ but sold at $\$24$. Another bookstore B sells this kind of book at $\$28$ after a percentage discount of $30\%$. And bookstore B offers a further percentage discount of $20\%$ on the part of purchasing beyond $100$ if customers purchase more than $100$ books of this kind.

Find the percentage discounts of the book at bookstore A.

Find the marked price of the book at bookstore B.

Find the selling price and the overall percentage discount of the book at bookstore B for the part of purchasing beyond $100$.

A school is planning to buy this kind of book for the students. Find which bookstore, A or B, has a cheaper total price if the school wants to buy $400$ such books.

Find the minimum number of books one will find it cheaper to buy from bookstore B than bookstore A.

<p>A storeowner buys a certain number of goods from supplier A at $\$6$ as a unit price and sell at $\$12$ as a unit price. The storeowner bears all other costs at $\$4,000$ in total. Suppose the owner manages to sell all the goods and earns a profit of $20\%$ on the total cost.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the number of goods the owner buys from supplier A.</span></div></li></ol>
<p>Another supplier B offers a lower unit price at $\$4$ to the storeowner. The storeowner buys a new number of such goods from supplier B and sell at the unit price $\$12$. But this time the storeowner only sells $45\%$ of the goods and made a loss of $10\%$ on the total cost. Suppose all other costs are also $\$4,000$ in total.</p>
<ol class="i-list" start="2"><li><div class="list-item-content"><span class="list-item-text">Find the new number of goods the owner buys from supplier B.</span></div></li></ol>

A storeowner buys a certain number of goods from supplier A at $\$6$ as a unit price and sell at $\$12$ as a unit price. The storeowner bears all other costs at $\$4,000$ in total. Suppose the owner manages to sell all the goods and earns a profit of $20\%$ on the total cost.

Find the number of goods the owner buys from supplier A.

Another supplier B offers a lower unit price at $\$4$ to the storeowner. The storeowner buys a new number of such goods from supplier B and sell at the unit price $\$12$. But this time the storeowner only sells $45\%$ of the goods and made a loss of $10\%$ on the total cost. Suppose all other costs are also $\$4,000$ in total.

Find the new number of goods the owner buys from supplier B.

 Percentages involving Finances: Profit and Loss

<p>A stationery vendor bought $500$ pencils at a total price of $\$300$ and sells the pencils at $\$1.00$ each. Find</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the cost of each pencil,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the profit as a percentage of the cost for each pencil (Correct your answer to $3$ significant figures),</span></div></li><li><div class="list-item-content"><span class="list-item-text">the number of pencils he has to sell to avoid making a loss,</span></div></li><li><div class="list-item-content"><span class="list-item-text">total amount of profit if all the pencils are sold,</span></div></li><li><div class="list-item-content"><span class="list-item-text">If $27$ of the pencils are damaged, which cannot be sold, find the new selling price of each pencil if the vendor intends to keep the same amount of profit. Round your answer to the nearest cent.</span></div></li></ol>

A stationery vendor bought $500$ pencils at a total price of $\$300$ and sells the pencils at $\$1.00$ each. Find

the profit as a percentage of the cost for each pencil (Correct your answer to $3$ significant figures),

the number of pencils he has to sell to avoid making a loss,

total amount of profit if all the pencils are sold,

If $27$ of the pencils are damaged, which cannot be sold, find the new selling price of each pencil if the vendor intends to keep the same amount of profit. Round your answer to the nearest cent.

<p>A factory buys raw materials at $\$25,000$ and pays salary to workers at $\$60,000$. The products are sold to a store at a profit of $15\%$ on the total cost.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the total selling price of the products by the factory.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Due to the increasing cost in raw materials, the factory makes a loss of $8\%$ on the total cost, given that the workers’ salary and selling price stay the same. Find the new price of raw materials.</span></div></li></ol>

A factory buys raw materials at $\$25,000$ and pays salary to workers at $\$60,000$. The products are sold to a store at a profit of $15\%$ on the total cost.

Find the total selling price of the products by the factory.

Due to the increasing cost in raw materials, the factory makes a loss of $8\%$ on the total cost, given that the workers’ salary and selling price stay the same. Find the new price of raw materials.

<p>A fruit vendor buys $1000$ packs of strawberry from a farmer at $\$5$ per pack. All other costs including delivery are $\$200$ in total. Suppose all packs of strawberry are sold.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the selling price per pack of strawberry if the vendor wants to earn a $60\%$ profit on his total cost.</span></div></li><li><div class="list-item-content"><span class="list-item-text">During delivery, $17$ packs of the strawberry are damaged, thus cannot be sold. Find the new selling price per pack of strawberry if the vendor wants to earn a same percentage of profit on his total cost. Round your answer to the nearest cent.</span></div></li></ol>

A fruit vendor buys $1000$ packs of strawberry from a farmer at $\$5$ per pack. All other costs including delivery are $\$200$ in total. Suppose all packs of strawberry are sold.

Find the selling price per pack of strawberry if the vendor wants to earn a $60\%$ profit on his total cost.

During delivery, $17$ packs of the strawberry are damaged, thus cannot be sold. Find the new selling price per pack of strawberry if the vendor wants to earn a same percentage of profit on his total cost. Round your answer to the nearest cent.

<p>Mrs. Lim bought a house at $\$550,000$ and spent $\$50,000$ on the redecoration. She then leased the house at $\$42,000$ per year for $10$ years. Then Mrs. Lim sold the house at $\$700,000$.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the total profit of Mrs. Lim as a percentage of her cost (Correct your answer to $3$ significant figures).</span></div></li><li><div class="list-item-content"><span class="list-item-text">If Mrs. Lim only lease the house without selling it, find the number of years after which Mrs. Lim will obtain a profit of $5\%$.</span></div></li></ol>

Mrs. Lim bought a house at $\$550,000$ and spent $\$50,000$ on the redecoration. She then leased the house at $\$42,000$ per year for $10$ years. Then Mrs. Lim sold the house at $\$700,000$.

Find the total profit of Mrs. Lim as a percentage of her cost (Correct your answer to $3$ significant figures).

If Mrs. Lim only lease the house without selling it, find the number of years after which Mrs. Lim will obtain a profit of $5\%$.

<p>A store manager first increased the price of their products by $60\%$, then lowered the price by $20\%$. A customer bought a specific product at $\$160$ as a current price.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the original price of the product.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the overall percentage change in the price of this product compared to its original price.</span></div></li></ol>

A store manager first increased the price of their products by $60\%$, then lowered the price by $20\%$. A customer bought a specific product at $\$160$ as a current price.

Find the overall percentage change in the price of this product compared to its original price.

 Percentage Change and Reverse Percentage

<p>Amy expected that her monthly income could be increased by $20\%$ this year compared to her monthly income last year, but due to company’s financial situation, her salary was cut down by $15\%$. As a result, Amy’s monthly salary was reduced by $\$1,680$ compared to her expectation.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the monthly income of Amy’s in the last year.</span></div></li><li><div class="list-item-content"><span class="list-item-text">When financial situation recovers, the company decides to increase Amy’s monthly income to her expectation. Find the percentage increase in Amy’s monthly income (Correct your answer to $3$ significant figures).</span></div></li></ol>

Amy expected that her monthly income could be increased by $20\%$ this year compared to her monthly income last year, but due to company’s financial situation, her salary was cut down by $15\%$. As a result, Amy’s monthly salary was reduced by $\$1,680$ compared to her expectation.

Find the monthly income of Amy’s in the last year.

When financial situation recovers, the company decides to increase Amy’s monthly income to her expectation. Find the percentage increase in Amy’s monthly income (Correct your answer to $3$ significant figures).

<p>The value of a machine depreciates by $50\%$ every year after its purchase. If the value of a machine is $\$250,000$ in the year $2020$, and the price was $\$2,000,000$ on purchase.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the year when the machine was purchased.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the year when the machine's value depreciates to $\$62,500$.</span></div></li></ol>

The value of a machine depreciates by $50\%$ every year after its purchase. If the value of a machine is $\$250,000$ in the year $2020$, and the price was $\$2,000,000$ on purchase.

Find the year when the machine was purchased.

Find the year when the machine's value depreciates to $\$62,500$.

<p>A house costs $\$300,000$ in the year $2010$, and the price increased by $20\%$ over the next $5$ years. Then the price further increased by $25\%$ over the next $5$ years. Find</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the prices of the house in the year $2015$ and the year $2020$, respectively,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the overall percentage of increase in the house's price from year $2010$ to $2020$.</span></div></li></ol>

A house costs $\$300,000$ in the year $2010$, and the price increased by $20\%$ over the next $5$ years. Then the price further increased by $25\%$ over the next $5$ years. Find

the prices of the house in the year $2015$ and the year $2020$, respectively,

the overall percentage of increase in the house's price from year $2010$ to $2020$.

<p>For two real numbers, $x$ and $y$, given that $x$ is $40\%$ of $y$, find</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the value of $\frac{x}{8y}$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">$(5x + y)$ as a percentage of $y$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">$x^2$ as a percentage of $y^2$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">$y^2$ as a percentage of $x^2$.</span></div></li></ol>

For two real numbers, $x$ and $y$, given that $x$ is $40\%$ of $y$, find

<p>The breadth of a cuboid is $6$ cm. The length of the cuboid is $150\%$ that of its breadth, and the breadth of the cuboid is $150\%$ that of its height.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the length and height of the cuboid.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the volume of the cuboid.</span></div></li><li><div class="list-item-content"><span class="list-item-text">If the length of the cuboid is increased by $50\%$ and the breadth of the cuboid is decreased by $50\%$, while the height of the cuboid does not change. Find the new length and breadth of the cuboid.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Based on your answers in (iii), determine whether the volume of the cuboid is the same as original. If yes, state your reasons by providing detailed workings. If not, find the new volume and the percentage change in the volume of the cuboid.</span></div></li></ol>

The breadth of a cuboid is $6$ cm. The length of the cuboid is $150\%$ that of its breadth, and the breadth of the cuboid is $150\%$ that of its height.

Find the length and height of the cuboid.

If the length of the cuboid is increased by $50\%$ and the breadth of the cuboid is decreased by $50\%$, while the height of the cuboid does not change. Find the new length and breadth of the cuboid.

Based on your answers in (iii), determine whether the volume of the cuboid is the same as original. If yes, state your reasons by providing detailed workings. If not, find the new volume and the percentage change in the volume of the cuboid.

Math Question Bank