Ratio P5 A001

Ali and Muthu share a sum of money. If Ali gives 1/2 of his share to Muthu, Muthu will have $48 more than Ali. If Ali gives 1/4 of his share to Muthu, Muthu will have $28 more than Ali. What is the ratio of Ali's share to Muthu's share?

Firstly given 1/2 and 1/4, make each unit the same. [1/2 x 2/2 = 2/4, denominator the same as 1/4 –-> Total 4 units for A.]

If Ali gives 1/2 of his share to Muthu, Muthu will have $48 more than Ali.
Then, draw A – 4 units with 2 units shaded and M – 2 units + $48.

A   [][][][]

M   [][][  48   ]

From above model, you can derive that originally M has $48.

If Ali gives 1/4 of his share to Muthu, Muthu will have $28 more than Ali.

Next draw A - 4 units with 1 unit shaded and M - 1 unit + $48. Then redraw M - 3 units + $28.

A   [][][][]

M   [][  48   ]

    [][][][ 28 ]

Compare M, you will get 2 units --> 48 – 28. [Difference of $48 and $28]

2 u -- > 48 – 28 = 20

1 u -- > 20 ÷ 2 = 10

A : 4 u -- > 10 x 4 = 40

M -- > 48

A : M = 40 : 48 = 5 : 6

The ratio of Ali's share to Muthu's share is 5 : 6.


Alternative method

Firstly given 1/2 and 1/4, make each unit the same. [1/2 x 2/2 = 2/4, denominator the same as 1/4 –-> Total 4 units for A.]

If Ali gives 1/2 (=2/4) of his share to Muthu, Muthu will have $48 more than Ali.

Ali will be left with 2 units, Muthu will have 2 units + $48. [Total is 4 units + $48]

If Ali gives 1/4 of his share to Muthu, Muthu will have $28 more than Ali.

Ali will be left with 3 units, Muthu will have 3 units + $28. . [Total is 6 units + $28]

As above involve units from Ali to Muthu, the Total remains a Constant [Constant Total].

6 u + 28 -- > 4 u + 48

2 u --> 48 – 28 = 20

1u --> 20 ÷ 2 = 10

A : 4 u --> 10 x 4 = 40

M --> 48

A : M = 40 : 48 = 5 : 6

The ratio of Ali's share to Muthu's share is 5 : 6.