Percentage P6 2010 SA2 Catholic High P2 Q??

Daniel had 40% more stickers than Brandon. Daniel and Brandon each gave 20% of their stickers to Calvin. As a result, Calvin's stickers increased by 80%. If Daniel has 20 more stickers than Calvin in the end, how many stickers did Brandon have at first?


B --> 100%
D --> 140%


20/100 x (100 + 140)% = 48%


80% --> 48%
100% --> 100/80 x 48% = 60%


DN --> 80/100 x 140% = 112%


CN --> 60% + 48% = 108%


(112 - 108)% = 4%


4% --> 20 stickers


100% --> 100/4 x 20 = 500 stickers


a) He had 500 stickers at first.

Percentage P6 2010 SA2 Catholic High P2 Q??

John had $180 more than Raymond at first. Both bought a different printer with some of their money. In the end, Raymond was left with $20 more than John. If John's printer cost 50% more than Raymond's printer, how much does John's printer cost?


J  [][                        ][                        ][                        ]
R [][$20]<--$180-->[                        ][                        ]


1 u --> 20 + 180 = 200

3 u --> 3 x 200 = $600

It costs $600.

Ratio P6 2010 SA2 Catholic High P2 Q??

At a conference made up of speakers and participants, there were 20% more men than women. The ratio of male speakers to female speakers was 8 : 5. There was an equal number of male and female participants.
a) Find the ratio of male speakers to male participants at the conference.
b) Halfway, 40 male participants left the conference and another 60 female participants joined the conference. In the end, there were 3/4 as many male participants as female participants remaining behind. How many speakers were there at the conference ?


M : F = 120 : 100
          = 6 : 5        Multiply by 3 to get difference of 3
         = 18 : 15     (equal to difference in speaker)

MS : FS = 8 : 5      Difference of 3 (8 - 5)

MP : FP = 1 : 1     Multiply by 10 so that totals tally
             = 10 : 10

MS : MP = 8 : 10
               = 4 : 5

a) It was 4 : 5.


 MP        FP
---------------
  10   :    10
- 40     + 60
---------------
   3    :     4
---------------

4 x (10 u - 40) --> 3 x (10 u + 60)
40 u - 160 --> 30 u + 180
10 u --> 180 + 160 = 340
1 u --> 340/10 = 34

13 u --> 13 x 34 = 442 speakers

a) There were 442 speakers.

Speed P6 2010 SA2 Catholic High P2 Q15

At 9am John was cycling from Point A to Point B. At the same time, Mary was cycling from point B to point A using the same route as John. Cycling at a speed of 4km/h faster than Mary, they would pass each other 300 meter away from the mid point.
a) What time did they pass each other?
b) If John took another 3 minutes to reach Point B, what time would Mary reach Point A?

 J
 -----> S + 4 km/h
9 am                       300 m 300 m |<----3 min----->|
 |----------------------|--------|--------|--------------------|
A             X                                  m           X        B
                                                                          9 am
                                                        S km/h <----
                                                                          M
                                                   |<--- 9 min ---->|

4000 m --> 60 min
600 m --> 600/4000 x 60 = 9 min

         9 min
 |----------------|
9 am             9.09 am

a) It was 9.09 am.


3 X --> X + 300 + 300        3 min versus 9 min
2 X --> 600
X --> 600/2 = 300 m

300 m --> 9 min
1200 m --> 1200/300 x 9 = 36 min

          36 min
    |--------------|
9 am          9.36 am

b) It was 9.36 am.