# IMAT 2012 Q24 [Ratios]

Tom shared out some money between his three children in the ratio 5:3:2. He later had an extra €6 which he gave to the child who received the least originally. This meant that the money had been shared into one large and two equal smaller shares.

How much money in total did Tom give to the three children?

A. €36
B. €26
C. €60
D. €20
E. €66

Simple steps to solve word problems:

• Underline key information
• Determine what they are trying to ask, and what you will need to solve it
• Eliminate any non-essential information
• Draw a picture, graph, or equation
• In moments of high stress like exam taking, always work with the paper they give you to avoid careless mistakes.
• Solve.

We know that we start with a 5:3:2 ratio, and then he gives €6 to the child who received the least. This will make the middle child have the same amount as the one who had the smallest amount originally, and we know this because it says the money has now been divided into one larger share (the 5 in the ratio) and two equal smaller shares.

We go from 3:2 ratio between the two smaller amounts to a 3:3 once we add €6. This must mean that 1/3 in this ratio =6. From this we can solve the problem.

(5)(€6)=€30

(3)(€6)=€18

(3)(€6)=€18

€30+18+18=€66

\fcolorbox{red}{grey!30}{Therefore the answer is E, €66.}