Question 11:
Diagram below shows two baskets of eggs.

(a) State the ratio of the number of chicken eggs to the number of duck eggs.
(b) A number of eggs need to be added into each basket so that the ratio in (a) remain unchanged. Find the minimum number of eggs to be added in each basket.

Solution: 
(a)
Ratio of the number of chicken eggs to the number of duck eggs
= 12 : 16
= 3 : 4

(b)
Let the number of eggs need to be added into each basket = n
Total number of eggs need to be added into each basket
= 3n + 4n

Minimum value of n = 1
Hence, the minimum number of eggs to be added into each basket
= 3(1) + 4(1)
= 3 + 4
= 7 (3 chicken eggs and 4 duck eggs need to be added to each basket)  

 

Question 12:
Diagram below shows two baskets, A and B, filled with candies.
(a) State the ratio of the number of candies in basket A to the number of candies in basket B.
(b) If 20 candies are added into basket A, calculate the number of candies which need to be added into basket B so that the ratio in (a) remain unchanged.

Solution: 
(a)
Ratio of the number of candies in basket A to the number of candies in basket B
= 10 : 12
= 5 : 6

(b)
If 20 candies are added into basket A, the number of candies which need to be added into basket B so that the ratio 5 : 6 remain unchanged
= 20 ÷ 5 × 6
= 4 × 6
= 24

 

Question 13:
Karim built two towers using toy bricks of the same size as shown in Diagram below.

(a) State the ratio of the number of toy bricks in Tower P to the number of toy bricks in Tower Q.
(b) A number of toy bricks need to be removed from each tower so that the ratio in (a) remains unchanged.
Find the total number of toy bricks to be removed from each tower.

Solution: 
(a)
Tower P : Tower Q
= 12 : 18
= 2 : 3

(b)
Let number of toy bricks to be removed from each tower = n
Total number of bricks to be removed
= 2n + 3n
2(1) + 3(1) = 2 + 3 = 5 → (2 bricks from tower P, 3 bricks from tower Q)
2(2) + 3(2) = 4 + 6 = 10 → (4 bricks from tower P, 6 bricks from tower Q)
2(3) + 3(3) = 6 + 9 = 15 → (6 bricks from tower P, 9 bricks from tower Q)
2(4) + 3(4) = 8 + 12 = 20 → (8 bricks from tower P, 12 bricks from tower Q)
2(5) + 3(5) = 10 + 15 = 25 → (10 bricks from tower P, 15 bricks from tower Q)

Question 6:
In a campaign of selling T shirt for Merdeka Day makes an amount of profit, RM x. The profit is divided between Jamal and Rafizi in the ratio of 5 : 3. Jamal receives RM 5400 more than Rafizi. Calculate the value of x.

Solution:
Portion of profit for Jamal = ⅝
Portion of profit for Rafizi = ⅜
Given Jamal receives RM 5400 more than Rafizi,
$\begin{array}{l}\frac{2}{8}\to \text{RM }5400\\ \therefore \frac{1}{8}\to \text{RM }5400÷2=\text{RM}2700\\ \\ x=2700\times 8\\ =21600\end{array}$

Question 7:
Karim and Roger share RM300 in the ratio of 2 : 3. Karim gives ⅓ of his share to Mandeep. Then Mandeep received RM60 from Roger.
Find the ratio of Karim’s money to roger’s money to Mandeep’s money.

Solution:
$\begin{array}{l}\text{Money received by Karim}\\ =\frac{2}{5}\times \text{RM}300\\ =\text{RM}120\\ \\ \text{Money received by Roger}\\ =\frac{3}{5}\times \text{RM}300\\ =\text{RM}180\\ \\ \text{Karim's money after given to Mandeep}\\ =\text{RM12}0\times \frac{2}{3}\\ =\text{RM}80\\ \\ \text{Roger's money after given to Mandeep}\\ =\text{RM18}0-\text{RM6}0\\ =\text{RM12}0\\ \\ \text{Mandeep's money}\\ =\text{RM}40+\text{RM}60\\ =\text{RM10}0\\ \\ \text{Ratio}=80:120:100\\ =4:6:5\end{array}$

Question 8:
Liza received three types of coloured marbles, red, green and yellow in the ratio of 2 : 5 : x. Given that the number of yellow marbles are more than the number of red marbles but less than the number of green marbles.
Calculate the number of yellow marbles that Liza received if the total number of marbles is 120.

Solution:
red : green : yellow = 2 : 5 : x
Given 2 < x < 5, so possible value of x is 3 in order to get a round number from the total of 120 marbles.

$\begin{array}{l}\frac{\text{yellow marbles}}{\text{total marbles}}=\frac{3}{2+5+3}\\ \frac{\text{yellow marbles}}{120}=\frac{3}{10}\\ \text{yellow marbles}=\frac{3}{10}\times 120\\ \text{yellow marbles}=36\end{array}$

Question 9:
John and Mahmud are required to draw a triangle ABC. The ratio of ∠A : ∠B : ∠C of the triangle drawn by John is 4 : 8 : 3 while the triangle drawn by Mahmud is 5 : 5 : 8.
Find the difference between the value of ∠B drawn by John and Mahmud.

Solution:
$\begin{array}{l}\angle B\text{ drawn by John}\\ =\frac{8}{4+8+3}\times {180}^o\\ ={96}^o\\ \\ \angle B\text{ drawn by Mahmud}\\ =\frac{5}{5+5+8}\times {180}^o\\ ={50}^o\end{array}$

Question 10:
The number of workers in an office building is 168 and they are placed in level two and level three. The number of workers in level three is 72.
(a) The ratio of workers in level two to level three is x : 3.
Find the value of x.
(b) 162 new workers have just started working in the office building. 3 of them are placed in level two, 93 in level three, while the rest is placed in level four.
Determine the ratio, in the lowest term of the workers of level two to three to four.

Solution:
$\begin{array}{l}\text{(a)}\\ \text{Ratio of workers in level two to level three}=x:3\\ x:3=\left(168-72\right):72\\ x:3=96:72\\ \frac{x}{3}=\frac{96}{72}\\ x=\frac{96}{72}\times 3\\ x=4\end{array}$

$\begin{array}{l}\text{(b)}\\ \text{Ratio of workers in level two to three to four}\\ =\left(96+3\right):\left(72+93\right):\left(162-3-93\right)\\ =99:165:66\\ =\frac{99}{33}:\frac{165}{33}:\frac{66}{33}\\ =3:5:2\end{array}$

$\begin{array}{l}\text{Given }x:y=4:5\text{ and }x+y=180\\ \frac{x}{x+y}=\frac{4}{4+5}\\ \frac{x}{180}=\frac{4}{9}\\ \therefore x=\frac{4}{9}\times 180\\ =80\end{array}$

$\begin{array}{l}\text{Given }x:y=9:5\text{ and }x-y=16\\ \frac{x+y}{x-y}=\frac{9+5}{9-5}\\ \frac{x+y}{16}=\frac{14}{4}\\ x+y=\frac{7}{2}\times 16\\ =56\\ x+y=56\end{array}$

Amy : Rizal : Muthu = 2 : 1 : 3
$\begin{array}{l}\frac{\text{Rizal}}{\text{Amy + Muthu}}=\frac{1}{2+3}\\ \frac{\text{Rizal}}{RM360}=\frac{1}{5}\\ \text{Rizal}=\frac{1}{5}\times RM360\\ =RM72\end{array}$

= 10 cm