F.1 Maths (Urgent, for Exam)

1. A retailer set the marked prices of all electronic goods 30% higher
than their costs. If all the goods were then sold at 30% discount, did
the retailer make a profit or a loss? What was the profit or loss
percentage?
The percentage change
= [1*(1+30%)*(1-30%)-1]/1 *100%
= (0.91-1)/1 *100%
= -9%
Hence, The retailer makes a loss for 9%
2. A computer shop bought 1000 printers at $1500 each, and 3000 boxes
of ink at $100 each. The shop sold the printers at $2800 each, and the
ink at a special price of $50 each if people bought the printer at the
same time. Find the profit percent after selling all the printers and
the boxes of ink at the special price?
The profit percent after selling all the printers and
the boxes of ink at the special price
= [-(1000)1500-(3000)100+(1000)2800+(3000)50]/[(1000)2800+(3000)50] *100%
= 40.0%(corr to 3sig fig)
3. An alloy contains 60% copper and 40% zinc by weight. Now there are
120 kg of the alloy, how much copper has to be added to lower the zinc
content to 30% and the percentage?
The original weight of copper = 120*0.6=72kg,i.e. weight of zinc = 120-72=48kg
Let x kg of copper is added,
(72+x)/0.7=120+x
72+x=84+0.7x
0.3x=12
x=40
Hence, the required amount needed to add is 40kg.
4. In the Legislative Council Election, there were 53278 registered
voters. If the voting rate was 71.81%, and one of the candidates got
53.21% of the total number of votes, how many votes did the candidate
actually get?
The candidate
actually get
= 53278*71.81%*53.21%
= 20358 votes (corr to the nearest 1 vote)
5. 1-[2x-(3x-5)-1]=0,
1-2x+3x-5=0,
x-4=0
x=4
28-[5x-(3x+2)+24]=0,
28-5x+3x+2-24=0,
-2x+6=0
x=3
2(x-1)-[5-(x+2)]=x+1-3(x-3)
2x-2-5+x+2=x+1-3x+9
3x-5=-2x+10
5x=15
x=3