Notice that Hafiz didn't pay for the present for the first 2 cases. His amount of money remained the same

Since he has 11 units for both ratios , Hafiz has 11 units of $ at first.

Now from the first case, Muthu has 9 units. He didn't pay as well so his $ also remained the same. So he also has 9 units at first.

Now from the second case, Darren didn't pay. Darren has 12 units of $. So this means he also has 12 units of money at first.

Ratio of their money at first D : M : H

= 12 : 9 : 11

Darren saved $36 more than Muthu. Difference = 12 units - 9 units = 3 units = $36

1 unit = $36 ÷ 3 = $12

From first case , the ratio is 4 : 9 : 11

Looking at Darren's ratio,

Cost of the present = 12 units - 4 units
= 8 units

= $12 x 8
= $96

Or

From second case, the ratio is 12 : 1 : 11

Looking at Muthu's ratio,

Cost of the present = 9 units - 1 unit
= 8 units

= $12 x 8
= $96

We don't actually need the last ratio and the information that they shared the cost of the gift equally to solve this question.

However, another way you can approach this question you can change the last ratio to make the units the same for Darren's amount of money at first.


4 : 3 : 1
= 12 : 9 : 3

Compare the following

① 4 : 9 : 11 (Muthu and Hafiz didn't pay)
② 12 : 1 : 11 (Darren and Hafiz didn't pay)
③ 12 : 9 : 3 (Darren and Muthu didn't pay)

And you get the ratio of their $ at first
(12 : 9 : 11)