Logo
Logout

Ratios, Rates and Best Buys - Questions

Question 1

Simplify the ratio \(21:28:42\)

\(3:4:6\)

Question 2

Simplify the following ratio.

\(500~\text{g}\) : \(2.2~\text{kg}\)

\(5:22\)

Question 3

Father divided the money among Max , Evie and Zoe in the ratio \(2 : 3 : 5\). If Zoe received $180, find the total amount and the money received by Max.

\(\$72\)

\begin{align} \text{Money received by Max} &\text{, Evie and Zoe are in ratio }2:3:5\\
\text{Total parts}& =10\\
\text{Money received by Max }&=2x,\text{ Evie }=3x \text{ and Zoe}=5x
\end{align}
\begin{align*} 5x&=180 \\
x&=36\\
\text{Total amount}&=36 \times 10\\
&=$360
\end{align*}\begin{align*} \text{Money received by Max}&=2x \\ &=2 \times 36 \\ &=72 \end{align*}

Question 4

Simplify \(4~\text{kg} : 400~\text{g}\)

\(10:1\)

Question 5

In a cricket match between India and Australia, Australia scored 280 runs in 50 overs while India made 281 runs in 45 overs.

a) What is the run rate of Australia?
b) What is the run rate of India?

\(a)~\text{5.6 runs/over}\)

\(b)~\text{6.24 runs/over}\)

Question 6

Which of the following is a better buy 

A pack of \({\rm{9}}\) toilet rolls costs \({\rm{\$ 4}}{\rm{.23}}\)

A pack of \({\rm{4}}\) toilet rolls costs \({\rm{\$ 1}}{\rm{.96}}\)

\(9~\rm{ pack}\)

Question 7

Henry and Isla won $90000 in a lottery. If they share the prize in the ratio \(36 : 54\), how much does Henry receive?

\(\$36000\)

\begin{align*} \text{Total number of parts} &=36+54 \\ &=90 \end{align*} \(\begin{aligned} \therefore \quad &90 \text{ parts}=90000 \\ &1 \text{ part}=1000 \end{aligned}\) \begin{align*} \text{Henry's share}&=36 \times 1000 \\ &=\$36000 \end{align*}

Question 8

A car maintains an average speed of 80 km/h. Calculate how far it will travel:

a. In 3 hours
b. From 3 pm to 8 pm

a) \(240~\text{km}\)   b) \(400~\text{km}\)

Question 9

Isabella earns $320 for an 9-hour day.

a. Express this pay as an hourly rate ($/h).
b. How much would she earn in a 50-hour week?
c. How many hours will it take her to earn $2100? Write the answer correct to 1 decimal place.

a) $35.56 / hour  b) $1778  c) 59.1 hours

Question 10

Potatoes cost \({\rm{\$ 18}}{\rm{.75}}\) for a \({\rm{12}}{\rm{.5 ~kg}}\) bag at a farm shop.The same type of potatoes cost \({\rm{\$ 4}}{\rm{.50}}\) for a \({\rm{ 2}}{\rm{.5 ~kg}}\) bag at a supermarket. Where are the potatoes the better value?

\({\rm{farm ~shop}}\)

Question 11

Determine the best buy \(15 \mathrm{~g}\) for \(\$ 4.95\) on \(25 \mathrm{~g}\) for \(\$ 9.50\)

\(15 \mathrm{~g}\)

Question 12

The ratio of a fathers age to the age of his daughter is \(11: 3\). If the father age is 44, find the age of the daughter.

12

Question 13

James' heart beats at 62 beats / min. How many times will it beat in 1 hour?

3720

Question 14

Birth rates are given as births \(/ 1000\) people. A city's birth rate is 14 births per 1000 people. If there were 560 births in the city last year, what is the population?

40000

Question 15

Determine the best buy: \(200 \mathrm{~mL}\) for \(\$ 8.50\) or \(500 \mathrm{ml}\) for \(\$ 20.80\).

\(500 \mathrm{~mL}\)

Question 16

Bird seed is sold in 3 sizes; \(500 \mathrm{~g}\) for \(\$ 1.80\), \(1 \mathrm{~kg}\) for \(\$ 3.40\) and \(1.75 \mathrm{~kg}\) for \(\$ 5.80\). Which size represents the better value?

\(1.75\mathrm{~kg}\)