4.2.2 Ratio, Rates and Proportions, PT3 Focus Practice - Mathematics

Question 5:

In diagram below, ABC is a triangle.

The sides of the triangle are in the ratio AB : BC: CA = 4 : 7 : 6.

Find the difference in length, in cm, between AB and CA.

Solution:

\begin{matrix} A B : B C : C A = 4 : 7 : 6 B C = 35 c m \frac{A B}{B C} = \frac{4}{7} \frac{A B}{35} = \frac{4}{7} A B = \frac{4}{7} \times 35 = 20 c m \frac{C A}{35} = \frac{6}{7} C A = \frac{6}{7} \times 35 = 30 c m \end{matrix}

$\begin{array}{l} A B : B C : C A = 4 : 7 : 6 \\ B C = 35 c m \\ \frac{A B}{B C} = \frac{4}{7} \\ \frac{A B}{35} = \frac{4}{7} \\ A B = \frac{4}{7} \times 35 \\ = 20 c m \\ \frac{C A}{35} = \frac{6}{7} \\ C A = \frac{6}{7} \times 35 \\ = 30 c m \end{array}$

Difference in length between AB and CA

= 30 – 20

= 10 cm

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{matrix} \frac{2}{8} \to RM 5400 ∴ \frac{1}{8} \to RM 5400 \div 2 = RM 2700 x = 2700 \times 8 = 21600 \end{matrix}

$\begin{array}{l} \frac{2}{8} \to RM 5400 \\ ∴ \frac{1}{8} \to RM 5400 \div 2 = RM 2700 \\ x = 2700 \times 8 \\ = 21600 \end{array}$

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

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

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