Teacher said that there were 100 students in his class, 24 of whom were boys and 32 were girls. Which base system did the teacher use in this statement?a)9b)5c)6d)8Correct answer is option 'C'. Can you explain this answer?

Question

Answer

We are provided with the equation (32) + (24) = (100). Let us assume our base be 'b'
Then,we can say:

⇒ 32 = 3 x b¹+ 2 x b⁰ = 3b+2
⇒ 24 = 2 x b¹+ 4 x b⁰= 2b+4
⇒ 100 = 1 x b²+ 0 x b¹+ 0 x b⁰ = b²

Now, according to our question:

⇒ 32 + 24=100
⇒ (3b + 2) + (2b + 4) = (b²)
⇒ 5b + 6 = b²
⇒ b²- 5b - 6 = 0
⇒ b²- 6b + b - 6 = 0
⇒ b(b - 6) + 1(b - 6) = 0
⇒ (b - 6) * (b + 1) = 0
⇒ b = 6,- 1

Base can't be negative. Hence b = 6.
∴ Base assumed in the asked question must be 6.

Answer

Given, 24+32= 100;
let the base be b;
so, (2b+4)+(3b+2)= b^2;
we get: 5b+6=b^2; solving;
b^2-5b-6=0;
b^2-6b+b-6=0;
b(b-6)+(b-6)=0,
(b-6)+(b+1)=0;
b=6 or b= -1;
since, base can't be negative (-1) so, answer is 6; op(c)

Answer

Given information:
- Total number of students in the class = 100
- Number of boys in the class = 24
- Number of girls in the class = 32

To determine which base system the teacher used in this statement, we need to look at the numbers provided and see if they fit within a particular base system.

In a base system, the digits are represented by numbers ranging from 0 to (base - 1). For example, in the decimal (base-10) system, the digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Let's check the given numbers in different base systems one by one:

a) Base-9 system
- In base-9 system, the digits are 0, 1, 2, 3, 4, 5, 6, 7, and 8.
- The number of students in the class cannot be represented in base-9 system using a single digit, as 100 is greater than the highest digit in this system (which is 8).
- Hence, option A is incorrect.

b) Base-5 system
- In base-5 system, the digits are 0, 1, 2, 3, and 4.
- The number of students in the class cannot be represented in base-5 system using a single digit, as 100 is greater than the highest digit in this system (which is 4).
- Hence, option B is incorrect.

c) Base-6 system
- In base-6 system, the digits are 0, 1, 2, 3, 4, and 5.
- The number of students in the class can be represented in base-6 system using three digits: 2 4 4.
- Similarly, the number of boys in the class can be represented in base-6 system using two digits: 1 0.
- And, the number of girls in the class can be represented in base-6 system using two digits: 2 2.
- Hence, option C is correct.

d) Base-8 system
- In base-8 system, the digits are 0, 1, 2, 3, 4, 5, 6, and 7.
- The number of students in the class cannot be represented in base-8 system using a single digit, as 100 is greater than the highest digit in this system (which is 7).
- Hence, option D is incorrect.

Therefore, the correct answer is option C, i.e., the teacher used the base-6 system in this statement.

Answer

Fgygtfhgf fvjj

Answer

9 correrect Answer • c. solution Answer is ' 6. Explanation. We are prouded the equation. (32)+(24)= (100). Let us assume our base be 'b'. Then ;we can say. 32=3×b1+2×b0=3b+2 similarly. 24= 2×b1+4×b0= 2b+4 100=1×b2+0+b1+0b0=b2Now. according to our question 32+24=100. ( 3b+2)+(2b+4)=(b2) 5b+6=b2. b2-5b-6=0. b2-6b+b-6=0. b(b-6)+1(b-6)=0. (b-6) (b+1)= 0 b=6,-1.

Answer

Ck

Answer

We are provided with the equation (32) + (24) = (100). Let us assume our base be 'b'
Then,we can say:

⇒ 32 = 3 x b¹+ 2 x b⁰ = 3b+2
⇒ 24 = 2 x b¹+ 4 x b⁰= 2b+4
⇒ 100 = 1 x b²+ 0 x b¹+ 0 x b⁰ = b²

Now, according to our question:

⇒ 32 + 24=100
⇒ (3b + 2) + (2b + 4) = (b²)
⇒ 5b + 6 = b²
⇒ b²- 5b - 6 = 0
⇒ b²- 6b + b - 6 = 0
⇒ b(b - 6) + 1(b - 6) = 0
⇒ (b - 6) * (b + 1) = 0
⇒ b = 6,- 1

Base can't be negative. Hence b = 6.
∴ Base assumed in the asked question must be 6.

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