Ratio P6 2010 SA2 Nanyang P2 Q17

There were some blue marbles and white marbles in a bag. If 70 blue marbles were to be removed from the bag, the ratio of the number of blue marbles to the number of white marbles would be 3 : 4. If 112 white marbles were to be removed from the bag instead, the ratio of the number of blue marbles to the number of white marbles would be 8 : 7. When 48 more blue marbles were to be added into the bag, what percentage of all the marbles would be blue marbles? [5 marks][Answer given: 49.6%]


B           W
- 70
--------------
 3      :    4
--------------

4 B - 4 x 70 --> 3 W

4 B --> 3 W + 280

28 B -->: 21 W + 7 x 280 = 21 W + 1960 


B            W
           - 112
---------------
8     :       7
---------------

7 B --> 8 W - 8 x 112 = 8 W - 896

28 B --> 32 W - 4 x 896 = 32 W - 3584


32 W - 3584 --> 21 W + 1960

11 W --> 1960 + 3584 = 5544

W --> 5544/11 = 504

4 B --> 3 x 504 + 280 = 1792

B --> 1792/4 = 448

448 + 48 = 496 blue marbles

496 + 504 = 1000

496/1000 x 100% = 49.6%

It was 49.6%.


Alternative method
----------------------

3 u + 70 --> 8 p

4 u - 112 --> 7 p

12 u --> 32 p - 4 x 70 = 32 p - 280

12 u --> 21 p + 3 x 112 = 21 p + 336

32 p - 280 --> 21 p + 336

11 p --> 336 + 280 = 616

1 p --> 616 / 11 = 46

8 p --> 8 x 56 = 448

448 + 48 = 496 blue marbles

15 p --> 15 x 56 = 840

840 + 112 + 48 = 1000 marbles

496/1000 x 100% = 49.6%

It was 49.6%.

Ratio P6 2010 SA2 Nanyang P1 Q21

The cost of 3 mangoes is the same as the cost of 5 grapefruits. The cost of 3 mangoes is also the same as the cost of 10 pears. Find the ratio of the cost of a mango to the cost of a grapefruit to the cost of a pear.
(Ans : 10 : 6 : 3)

3 M --> 5 G

M/G --> 5/3 = 10/6


3 M --> 10 P

M/P --> 10/3

M : G : P = 10 : 6 : 3


Alternative method
----------------------
Assume 3 mangoes = 5 grapefruits = 10 pears = $1
1 M --> 1/3

1 G --> 1/5

1 P --> 1/10

M : G : P = 1/3 : 1/5 : 1/10
               = 10 : 6 : 3    Multiply by 30

Ratio P6 2009 SA2 P2 Nanyang Q12

Given that p : (q + r) = 1 : 3, r : (q + s) = 1 : 2 and p : s = 2 : 5.
(a) Find p : q : r : s.
(b) Find (r + q) : (p + s).

                   x 3
p : s = 2 : 5 = 6 : 15

                           x 2       x 3 
p : (q + r) = 1 : 3 = 2 : 6 = 6 : 18

                                            x 3
s + (q + r) = 5 + 6 = 11 ............... 33

                          x 11 
r : (q + s) = 1 : 2 = 11 : 22

s = 15, (q + s) = 22, so q = 22 - 15 = 7

a) p : q : r : s = 6 : 7 : 11 : 15

b) (r + q) : (p + s) = (11 + 7) : (6 + 15)
                             = 18 : 21
                             = 6 : 7