Teacher distributes ‘N’ chocolates to ‘3x’ students. Find the value of *x*.

Given statements:

A. If he distributes 6 chocolates to each student, then teacher is left with 24 chocolates.

B. If the number of students were $\frac{1}{3}$ of original number, then no chocolate was left with the teacher.

C. $30

Question

Teacher distributes ‘N’ chocolates to ‘3x’ students. Find the value of *x*.

Given statements:

A. If he distributes 6 chocolates to each student, then teacher is left with 24 chocolates.

B. If the number of students were $\frac{1}{3}$ of original number, then no chocolate was left with the teacher.

C. $30 < $ number of students $< 40$ and $200 < $ number of chocolates $< 300$.

Which of the following options is correct?

Accepted Answer

**Solution:**

Let the number of students be $3x$ and the total chocolates be $N$.

**From statement A:**
- Each student gets 6 chocolates, leftover chocolates = 24
- So, total chocolates distributed = $6 	imes 3x = 18x$
- Total chocolates $N = 18x + 24$

**From statement B:**
- Number of students is $\frac{1}{3}$ of original, i.e., $x$ students
- No chocolates left, so $N$ is divisible by $x$
- Total chocolates $N = 6x$ (since each student gets 6 chocolates)

Equate $N$ from A and B:

$$18x + 24 = 6x \implies 12x = -24 \implies x = -2$$

Since $x$ cannot be negative, statements A and B together are inconsistent and cannot find $x$.

**From statements B & C:**
- Number of students $3x$ satisfies $30 < 3x < 40$ so $10 < x < \frac{40}{3} \approx 13.33$
- Number of chocolates $N$ satisfies $200 < N < 300$

From B, $N = 6x$ (since $N$ divisible by $x$ and $N=6x$)

Check possible integer values of $x$ in range 11, 12, 13:
- For $x=11$, $N=66$ (not in 200-300)
- For $x=12$, $N=72$ (not in 200-300)
- For $x=13$, $N=78$ (not in 200-300)

No value satisfies the range for $N$, so B & C together cannot find $x$.

**From statements A & C:**
- From A, $N = 18x + 24$
- From C, $30 < 3x < 40 \implies 10 < x < 13.33$
- Also, $200 < N < 300$

Calculate bounds for $N$:

$$18 	imes 10 + 24 = 180 + 24 = 204$$
$$18 	imes 13 + 24 = 234 + 24 = 258$$

So, $204 < N < 258$ which fits in $200 < N < 300$

Possible $x$ values are integers 11, 12, 13 but multiple values satisfy the condition, so exact $x$ cannot be found.

**Conclusion:**
- None of the pairs of statements can uniquely determine $x$.

**Answer:** None of the given statements can answer the question.

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