HomeNon-Routine MathematicsThe Famous Rabbit and Chicken ...

## How to Solve Without Algebraic Equations

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