Question 15:
Table 4 shows information about four ingredients used to make a type of cake.
(a) Find the value of x and of y. [3 marks]
(b) The composite index for the cost of making the cake in the year 2023 with 2021 as the base year is 127.5. The ratio of the ingredients A, B, C and D used is 3 : 2 : m : 4..
Find the value of m.
[2 marks]
(c) It is expected that the price of the cake will increase by 20% from the year 2023 to the year 2025.
(i) Find the composite index for the cost of making the cake in the year 2025 with 2021 as the base year.
(ii) State the price of the cake in the year 2025, if the price in the year 2021 is RM100 per kg.
(iii) Find the percentage increase of ingredient C from the year 2021 to the year 2025 if the price of other ingredients remains unchanged from the year 2023 to the year 2025.
[5 marks]
Answer:
(a)
$$ \begin{aligned} x & =\frac{27.5}{25} \times 100 \\ & =110 \end{aligned} $$
$$ \begin{aligned} \frac{22.5}{y} \times 100 & =150 \\ \frac{22.5}{y} & =1.5 \\ y & =15 \end{aligned} $$
(b)
$$ \begin{aligned} \frac{(3)(110)+(2)(112.5)+(m)(150)+(4)(120)}{3+2+m+4} & =127.5 \\ \frac{1035+150 m}{9+m} & =127.5 \\ 1035+150 m & =1147.5+127.5 m \\ 22.5 m & =112.5 \\ m & =5 \end{aligned} $$
(c)(i)
$$ \begin{aligned} & \bar{I}_{2025 / 2021}=127.5 \times \frac{120}{100} \\ & \bar{I}_{2025 / 2021}=153 \end{aligned} $$
(c)(ii)
$$ \begin{aligned} \frac{P_{2025}}{100} \times 100 & =153 \\ P_{2025} & =\text { RM } 153 \end{aligned} $$
(c)(iii)
$$ \begin{aligned} \frac{(3)(110)+(2)(112.5)+(5)\left(I_{\mathrm{C}}\right)+(4)(120)}{3+2+5+4} & =153 \\ \frac{1035+5 I_{\mathrm{C}}}{14} & =153 \\ 1035+5 I_{\mathrm{C}} & =2142 \\ 5 I_{\mathrm{C}} & =1107 \\ I_{\mathrm{C}} & =221.4 \end{aligned} $$
$$ \begin{aligned} \frac{P_{2025}}{15} \times 100 & =221.4 \\ P_{2025} & =\mathrm{RM} 33.21 \\ \frac{33.21-15}{15} & \times 100 \%=121.4 \% \end{aligned} $$
Table 4 shows information about four ingredients used to make a type of cake.
(a) Find the value of x and of y. [3 marks]
(b) The composite index for the cost of making the cake in the year 2023 with 2021 as the base year is 127.5. The ratio of the ingredients A, B, C and D used is 3 : 2 : m : 4..
Find the value of m.
[2 marks]
(c) It is expected that the price of the cake will increase by 20% from the year 2023 to the year 2025.
(i) Find the composite index for the cost of making the cake in the year 2025 with 2021 as the base year.
(ii) State the price of the cake in the year 2025, if the price in the year 2021 is RM100 per kg.
(iii) Find the percentage increase of ingredient C from the year 2021 to the year 2025 if the price of other ingredients remains unchanged from the year 2023 to the year 2025.
[5 marks]
Answer:
(a)
$$ \begin{aligned} x & =\frac{27.5}{25} \times 100 \\ & =110 \end{aligned} $$
$$ \begin{aligned} \frac{22.5}{y} \times 100 & =150 \\ \frac{22.5}{y} & =1.5 \\ y & =15 \end{aligned} $$
(b)
$$ \begin{aligned} \frac{(3)(110)+(2)(112.5)+(m)(150)+(4)(120)}{3+2+m+4} & =127.5 \\ \frac{1035+150 m}{9+m} & =127.5 \\ 1035+150 m & =1147.5+127.5 m \\ 22.5 m & =112.5 \\ m & =5 \end{aligned} $$
(c)(i)
$$ \begin{aligned} & \bar{I}_{2025 / 2021}=127.5 \times \frac{120}{100} \\ & \bar{I}_{2025 / 2021}=153 \end{aligned} $$
(c)(ii)
$$ \begin{aligned} \frac{P_{2025}}{100} \times 100 & =153 \\ P_{2025} & =\text { RM } 153 \end{aligned} $$
(c)(iii)
$$ \begin{aligned} \frac{(3)(110)+(2)(112.5)+(5)\left(I_{\mathrm{C}}\right)+(4)(120)}{3+2+5+4} & =153 \\ \frac{1035+5 I_{\mathrm{C}}}{14} & =153 \\ 1035+5 I_{\mathrm{C}} & =2142 \\ 5 I_{\mathrm{C}} & =1107 \\ I_{\mathrm{C}} & =221.4 \end{aligned} $$
$$ \begin{aligned} \frac{P_{2025}}{15} \times 100 & =221.4 \\ P_{2025} & =\mathrm{RM} 33.21 \\ \frac{33.21-15}{15} & \times 100 \%=121.4 \% \end{aligned} $$