Ratio for 1st case = 4 : 9 : 11
Ratio for 2nd case = 12 : 1 : 11
Ratio for 3rd case = 4 : 3 : 1


Realise that for the first two cases, Hafiz's savings is the same at 11 units. He didn't spent anything for these two cases, so we can say Hafiz has 11 units.

For the 2nd and 3rd case, Darren did not spend any money.

We have 12 : 1 : 11 and
4 : 3 : 1

Since Darren did not spend any money, we have to make the units the same for Darren for both ratios.

4 : 3 : 1 = 12 : 9 : 3.

So Darren has 12 units.

For the 1st case , the ratio was 4 : 9 : 11. Comparing this to 12 : 9 : 3, this also tells you that Muthu had 9 units at first. And this makes sense as it shows Muthu did not spend in 1st and 3rd cases.


So ratio of their money at first
= 12 : 9 : 11


Difference vetween Darren and Muthu's savings = 12 units - 9 units = 3 units

3 units = $36
1 unit = $36 ÷ 3 = $12

If we compare the ratios for each individual before and after spending.

Difference for Darren = 12 units - 4 units = 8 units
Difference for Muthu = 9 units - 1 unit = 8 units
Difference for Hafiz = 11 units - 3 units = 8 units

This tells you that each spent the same amount on the gift , 8 units. Remember that the gift's price doesn't change and is the same no matter who buys it.


So cost of gift = 8 x $12 = $96