A Math

A Math (IGCSE)

E Math

E Math (IGCSE)

H1 Math

H2 Math

IB AA HL Math

IB AA SL Math

IB AI HL Math

IB AI SL Math

IP Math

N(A) A Math

N(A) E Math

PSLE

PSLE Foundation Mathematics

<p>Ali, David and Priya agree to invest $\$315\,000$, $\$420\,000$ and $\$285\,000$ respectively into a project, and they cooperate with a technological university to develop their project. The university does not invest money into the project but will share $20\%$ of the profit of this project. The rest of the profit will be shared by Ali, David and Priya according to the ratio of their investments.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the ratio of Ali, David and Priya’s investments in the simplest form.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the fraction of total profit that Ali, David and Priya share, respectively.</span></div></li></ol>
<p>Suppose the project yields a total profit of $\$2\,550\,000$.</p>
<ol class="i-list" start="3"><li><div class="list-item-content"><span class="list-item-text">Find the amount of profit that Ali, David, Priya and the university received, respectively.</span></div></li></ol>

Ali, David and Priya agree to invest $\$315\,000$, $\$420\,000$ and $\$285\,000$ respectively into a project, and they cooperate with a technological university to develop their project. The university does not invest money into the project but will share $20\%$ of the profit of this project. The rest of the profit will be shared by Ali, David and Priya according to the ratio of their investments.

Find the ratio of Ali, David and Priya’s investments in the simplest form.

Find the fraction of total profit that Ali, David and Priya share, respectively.

Suppose the project yields a total profit of $\$2\,550\,000$.

Find the amount of profit that Ali, David, Priya and the university received, respectively.

Dividing Quantities in a Given Ratio

Percentage of a Quantity

Simplifying Ratios

Ratio

Ratio, Rate and Speed

Percentages

<p>In a research group, $40\%$ of the male members and $\frac{1}{4}$ of the female members undertake the theoretical study, while the rest of the members undertake the experimental study. The ratio of number of male members to the number of female members is $3 : 4$.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">For the members who undertake the experimental study, find the ratio of the number of male members to the number of female members.</span></div></li></ol>
<p>If the research group recruits $10$ more male members and $5$ more female members, the ratio of number of male members to the number of female members will be $1 : 1$.</p>
<ol class="i-list" start="2"><li><div class="list-item-content"><span class="list-item-text">Find the original number of male members and female members of the research group, respectively.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Hence find the original number of members who undertake theoretical study and the original number of members who undertake the experimental study.</span></div></li></ol>

In a research group, $40\%$ of the male members and $\frac{1}{4}$ of the female members undertake the theoretical study, while the rest of the members undertake the experimental study. The ratio of number of male members to the number of female members is $3 : 4$.

For the members who undertake the experimental study, find the ratio of the number of male members to the number of female members.

If the research group recruits $10$ more male members and $5$ more female members, the ratio of number of male members to the number of female members will be $1 : 1$.

Find the original number of male members and female members of the research group, respectively.

Hence find the original number of members who undertake theoretical study and the original number of members who undertake the experimental study.

Changing Ratios

<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.

Expressing One Quantity as a Percentage of Another

Application of Simultaneous Equations in Real World Contexts

 Basics of Percentage

Simultaneous Equations

<p>For two real numbers $x$ and $y$, where&nbsp;$y\ne0$, given that&nbsp;$x$ is $40\%$ of $y$, find</p>
<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">the value of $\frac{x}{8y}$,</div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">$(5x + y)$ as a percentage of $y$,</div></li><li data-list-item-id="item-iii" data-list-item-path="item-iii"><div class="list-item-paragraph">$x^2$ as a percentage of $y^2$,</div></li><li data-list-item-id="item-iv" data-list-item-path="item-iv"><div class="list-item-paragraph">$y^2$ as a percentage of $x^2$.</div></li></ol>

For two real numbers $x$ and $y$, where $y\ne0$, given that $x$ is $40\%$ of $y$, find

Basics of Percentage

<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.

Percentage Increase and Decrease

 Percentage Change and Reverse Percentage

<p>In a school of $550$ students, $40\%$ of them are boys. Find</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the number of boys in the school,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the number of girls in the school.</span></div></li></ol>

In a school of $550$ students, $40\%$ of them are boys. Find

<p>There are $800$ students in a school.</p>
<ol class="abc-list"><li data-list-item-id="item-1763960361934-ukblnj62z" data-list-item-path="item-1763960361934-ukblnj62z"><div class="list-item-paragraph">On a particular day, $18\%$ of the students were late for a school event. Calculate the number of students who were not late (on time or early).</div></li><li data-list-item-id="item-1763960362519-mlibb7bxq" data-list-item-path="item-1763960362519-mlibb7bxq"><div class="list-item-paragraph">In a particular semester, $35$ international students joined the school. Calculate the percentage increase in the number of students.</div></li></ol>

Basics of Percentage Change

<p>Angela’s monthly salary is $\$2500$.  She spends $75\%$ of her salary and saves the rest.</p>
<p>Elaine’s monthly salary is $\$1800$.  She spends $\$1200$ and saves the rest.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Find the amount that Angela spends every month.</div></li><li><div class="list-item-paragraph">Who saves a higher percentage of their monthly salary? Explain with workings.</div></li></ol>

Angela’s monthly salary is $\$2500$.  She spends $75\%$ of her salary and saves the rest.

Elaine’s monthly salary is $\$1800$.  She spends $\$1200$ and saves the rest.

Percentage Application: Spending and Savings

<p>A cohort of $140$ students, given that&nbsp;$75\%$ of them passed an English Test, calculate the number of students who failed the test.</p>

A cohort of $140$ students, given that $75\%$ of them passed an English Test, calculate the number of students who failed the test.

Percentage Application: Pass and Fail Rates

<p>In a class of $45$ students, $60\%$ of them are boys. Find </p>
<ol class="i-list"><li><div class="list-item-paragraph">percentage of girls in the class,</div></li><li><div class="list-item-paragraph">number of boys in the class. </div></li></ol>

In a class of $45$ students, $60\%$ of them are boys. Find 

Finding a Quantity based on its Percentage

<p>Ali, David and Priya agree to invest $\$315\,000$, $\$420\,000$ and $\$285\,000$ respectively into a project, and they cooperate with a technological university to develop their project. The university does not invest money into the project but will share $20\%$ of the profit of this project. The rest of the profit will be shared by Ali, David and Priya according to the ratio of their investments.</p>
<ol class="i-list"><li><div class="list-item-paragraph">Find the ratio of Ali, David and Priya’s investments in the simplest form.</div></li><li><div class="list-item-paragraph">Find the fraction of total profit that Ali, David and Priya share, respectively.</div></li></ol>
<p>Suppose the project yields a total profit of $\$2\,550\,000$.</p>
<ol class="i-list" start="3"><li><div class="list-item-paragraph">Find the amount of profit that Ali, David, Priya and the university received, respectively.</div></li></ol>

IP1U9 Exercise Q2

<p>A water tank is ${70\%}$ full. ${15\%}$ of the water in the tank is used. There is now ${476}$ litres of water in the tank. Calculate the capacity of the water tank.</p><p style="text-align: right;">[2]</p>

A water tank is ${70\%}$ full. ${15\%}$ of the water in the tank is used. There is now ${476}$ litres of water in the tank. Calculate the capacity of the water tank.

Math Question Bank