The blog postings are about the Singapore Math. The readers can learn from the postings about Solving Singapore Primary School Mathematics. The blog presents the Math Concept, the Math Questions with solutions that teaches in Singapore Primary Schools. You or the kids can aquire the skills of dealing with the Math Modeling, the Math Problem Solving and the Problem Sum from Lower Primary School to Upper Primary School level after reading the blog postings. This posting is an upper primary school math question on Percentage, Ratio and Problem Sum.

Read the posting on **Fatimah and Hairu play Congkak** to know about Congkak game.

Read the posting on **Sarin learns Average Number, Percentage and Charting in school (Math Concept)** to know about Percentage.

Read also the posting on **Sarin learns the concept of Ratio (mathematics concept)** to understand Ratio.

*Challenge yourself with the question before look for the given solution‼!*

**Upper primary school mathematics question UPQ485**

In a CongKak Game, Fatimah had 80% as many marbles as Hairu at the start of the game. Fatimah lost 75% of her marbles to Hairu during the first game. Hairu then lost 25% of his marbles to Fatimah during the second game. If Fatimah had 258 marbles at the end of the second game, how many marbles did Hairu have at first? Who won the CongKak Game?

* *Solution:

75% of 80% ==> 0.75 × 80% = 60%

After 1^{st} round,

The percentage of marbles Fatimah left with = 80% – 60% = 20%

The percentage of marbles Hairu had after 1 st round = 100% + 60% = 160%

In 2^{nd} round,

Hairu lost 25% of his marbles to Fatimah

25% of 160% ==> 0.25 × 160% = 40%

The percentage of marbles Hairu left with = 160% – 40% = 120%

The percentage of marbles Fatimah had after 2^{nd} round = 20% + 40% = 60%

Fatimah had 258 marbles at the end

60% ==> 258

10% ==> 43

100% ==> 430

The number of marbles Hairu had at first = 430

Hairu had won the game.

Alternative Solution(1):

Before the CongKak Game,

Fatimah’s marbles is 80% of Hairu’s marbles

Fatimah’s marbles : Hairu’s marbles = 80 : 100 = 4 : 5 = 100 : 125

Fatimah lost 75% of her marbles to Hairu after 1 game

The ratio after game 1

Fatimah’s marbles : Hairu’ marbles = 25 : 200

Hairu then lost 25% of his marble to Fatimah

Fatimah’s marbles : Hairu’s marbles = 75 : 150 = 1 : 2

The number of marble Fatimah left at the end = 258

The number of marbles Hairu left at the end = 2 × 258 = 516

The number of marbles Hairu left after 1^{st} game = 516 × 200/150 = 688

The number of marbles Hairu had at first = 688 × 125/200 = 430

Hairu had won the game.

Alternative Solution(2):

Before the CongKak Game,

Fatimah’s marbles is 80% of Hairu’s marbles

Fatimah’s marbles : Hairu’s marbles : Total = 80 : 100 : 180 = 4 : 5 : 9

Fatimah lost 75% of her marbles to Hairu after 1 game

The ratio after game 1,

Fatimah’s marbles : Hairu’ marbles = 4 × 0.25 : 5 + 4 × 0.75 : 9 = 1 : 8 : 9

Hairu then lost 25% of his marble to Fatimah after game 2

The ratio after game 2,

Fatimah’s marbles : Hairu’s marbles = 1 + 8 × 0.25 : 8 × 0.75 : 9 = 3 : 6 : 9

The number of marbles Fatimah left at the end = 258

The model of final ratio,

3 units = 258

1 unit = 86

The number of marbles Hairu had at first = 5 × 86 = 430

Hairu had won the game.