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SPM Additional Mathematics 2019, Paper 2 (Question 15)


Question 15:
Table 3 shows information related to five cake ingredients J, K, L, M and N used by a baker in his business.

Table 3

The composite index for the cost of making the cakes in the year 2020 based on the year 2016 is 136.
(a)(i) Find the value of x and of y.
(ii) Calculate the price for ingredient M in the year 2016 if the price in the year 2020 is RM6.30.
[4 marks]

(b) Calculate the value of p.   [3 marks]

(c) The cost of baking a cake in the year 2016 is RM25.
Find the selling price of a cake made in the year 2020, if the baker intends to make a profit of 80%.         [3 marks]


Solution:
(a)(i)
P2018P2016×100=115,P2020P2018×100=140x=P2020P2016×100  =P2020P2018×P2018P2016×100  =1.40×115  =161y=P2020P2016×100  =P2020P2018×P2018P2016×100  =0.90×140  =126

(a)(ii)
For ingredient M,P2020P2016×100=126RM6.30P2016×100=126P2016=RM6.30126×100       =RM5

(b)
Composite index=136IWW=136(124)(5)+(161)(6)+(130)(p)+(126)(4)+(120)(2)5+6+p+4+2=136130p+2330=136(17+p)130p+2330=2312+136p6p=18p=3

(c)
Cost price of a cake=RM25×1.36                               =RM34Selling price=180%×RM34                   =180100×RM34                   =RM61.20

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