Raffles Girls’ Primary School P5 SA1 2007 Math Question

Adam and Ben each have some money. If Adam spends $4, the ratio of the amount of money Adam has to the amount that Ben has will be 3:5. If Ben spends $4, the ratio of the amount of money Adam has to the amount that Ben has will be 11:13. How much money does each boy have?


(click on image to enlarge)


- If Adam spends $4, the ratio of the amount of money Adam has to the amount that Ben has will be 3:5, hence,

Adam has 3 units (after $4 spent), while Ben has 5 units (marked in blue in illustration above).


- If Ben spends $4, the ratio of the amount of money Adam has to the amount that Ben has will be 11:13, hence,

Adam now has been allocated 11 parts, while Ben has been allocated 13 parts (after $4 spent by Ben), as marked in red in llustration above.


From here, we can deduce

2 units ----- $4 + 2 parts $4
2 units ----- $8 + 2 parts
1 unit ----- $4 + 1 parts
3 units ----- $12 + 3 parts (*)


However, we know that
(Adam) 3 units ----- 11 parts - $4 (#) (as from model above)


Both * and # have an equivalent of 3 units. Therefore,

$12 + 3 parts (*) ----- 11 parts - $4 (#)
$16 ----- 8 parts
1 part ----- $16 divided by 8 = $2


Adam has ---- 11 parts
= (11 parts x $2)
= $22

Ben has ----- 13 parts + $4
= (13 parts x $2) + $4
= $26 + $4
= $30

Answer: Adam has $22, while Ben has $30.