Just back from Maths workshop by Ernest Wong this afternoon.
Useful bags and boxes method (Raffles Maths Trick Vol 1 Trick 2)
for solving word problems involving 2 pairs of ratios.

http://www.moe.gov.sg/education/syllabuses/sciences/files/maths-primary-2007.pdf

Question:

The ratio of the number of apples and oranges in a shop is 10:3.

When 50 apples and 40 oranges were added, the new ratio became 3:1.

How many apples were in the shop at first?

Solution:

Put the apples and oranges in bags and boxes.

Each bag contains the SAME number of fruits (apples or oranges)

Each box containsthe SAME number of fruits (apples or oranges)

Each bag many contain more or less fruits than each box (Not Equal)

At first ratio of apples to oranges was 10:3 (Bags)

Finally ratio of apples to oranges was 3:1 (Boxes)

Let there be 10 bags of apples and 3 bags of oranges

Let there be 3 boxes of apples and 1 box of oranges finally.

Fruits                                   Apple Oranges

Bags                                         10              3

Fruits added                      +50              +40

Boxes                                         3               1

Apples   ===> 10 bags + 50 –> 3 boxes

Oranges ===>  3 bags + 40 –> 1 box

or    9 bags + 120–>3  boxes

Boxes have same amount of apples and oranges,

so 9 bags + 120 = 10 bags +50  ===> 1 bag = 70

Apples at first = 10 bags or 700.

Answer check:

At first : Apples = 700  Oranges = 210  (Ratio 10:3 ok)

Later Apples = 750 Oranges =250 (Ratio 3:1 ok)