Singapore Maths
A logical and easier way of solving simultaneous equations based problems without using algebraic equations.
The Famous Rabbit and Chicken problem
Example:
There are some rabbits and chickens in a barn. What is the number of chickens if there are 396 legs and 150 heads in the barn?
Solution:
Using Non- Routine Logic:
There are 150 animals ( there are 150 heads)
Each animal has minimum 2 legs .
Chickens have 2 legs and rabbit have 2+2=4 legs
If all animals were chickens, then the number of legs= 150×2=300
But actual number of legs = 396
So, extra legs = 396-300=96
Each pair of extra legs belongs to a rabbit or each rabbit contributes 2 extra legs to the leg count.
Therefore, number of rabbits= number of extra legs ÷2= 96÷2 = 48
Number of chickens= 150 – 48= 102
Number of rabbits= 150 -102=48
Using Math:
Let number of chickens = x , number of Rabbits =y
Total number of animals x + y = 150 ———Eq i
Total number of legs 2x + 4y = 396 ———Eq ii
Substituting y= 150 – x (from Eq i) in Eq ii , we get
2x + 4 (150 – x) =396
600 – 396 = 2x
x = 204 ÷ 2=102
Number of chickens x=102
Number of rabbits= 150 – 102 = 48
Example:
Remi has Rs 240 in denominations of 20- and 10-rupee notes. Calculate the number of 20- and 10-rupee notes if the total number of notes is 16 .
Solution:
Using Non-Routine Logic :
If all 16 notes were 10 Rupee notes, then total amount will be Rs 160.
But total amount is Rs 240
Therefore, excessive amount =240 – 160 = Rs 80
Each extra value of Rs10 is coming from a 20 rupee note. Therefore, there are
80 ÷10 = 8 notes of Rs 20.
Number of Rs 20 Notes=8
Number of Rs 10 Notes=16 – 8 = 8
Using Math:
Let number of Rs 20 notes = x , number of Rs 10 notes =y
Total number of notes x + y = 16—————-Eq i
Total value of money 20x + 10y = 240———-Eq ii
Substituting x= 16-y (from Eq i) in Eq ii , we get
20 (16-y) + 10y =240
320 – 10y = 240
y= (320 – 240) ÷10 = 8
Number of 10 Rupee Notes = y = 8
Number of 20-rupee notes=x= 16 – 8 = 8
Example:
There are 35 questions in a test.6 marks are awarded for each correct answer and 2 marks are deducted for each wrong answer. Amar attempted all the questions and got 178 marks .How many questions did he answered correctly?
Solution:
Using Non-Routine Logic
Marks scored for 35 correct answers = 35 x 6= 210
Marks scored by Amar=178
Difference between maximum marks and marks scored by Amar=210 – 178=32
Marks lost for each wrong question = 6 – ( – 2)=8
Number of wrong answers= marks lost ÷ 8 = 32 ÷ 8 = 4
Number of correct Answers = 35 – 4 =31
