In the given question two quantities are given one as quantity -I and the other is quantity II you have to determine relationship between these two quantities and choose the appropriate options as given

Quantity-I:the present ratio of ages of kumar and simran is 11:12 and the ratio of ages of kumar's 2 year back to that of simran's 6 year hence is 2:3. find the age of kumar after 6 years

Quantity II:the average age of 20 students in class is 21 the teacher of class joined 35 years ago. Suppose the age of teacher is also included then the average age is increased by 2 years what was age of teacher when he joined the school

Options

A. `quantity-IgtII`
B. `quantity IltII`
C. `quantity IleII`
D. `quantity I=II`

Answer

To solve the problem, we need to analyze both Quantity-I and Quantity-II step by step.

### Quantity-I:

1. **Understanding the Age Ratio**:
- The present ratio of ages of Kumar and Simran is given as 11:12.
- We can denote Kumar's age as \(11x\) and Simran's age as \(12x\).

2. **Age Two Years Back and Six Years Hence**:
- Kumar's age 2 years back: \(11x - 2\)
- Simran's age 6 years hence: \(12x + 6\)

3. **Setting up the Ratio**:
- The ratio of Kumar's age 2 years back to Simran's age 6 years hence is given as 2:3.
- Therefore, we can write the equation:
\[ \frac{11x - 2}{12x + 6} = \frac{2}{3} \]

4. **Cross-Multiplying**:
- Cross-multiplying gives us:
\[ 3(11x - 2) = 2(12x + 6) \]
- Expanding both sides:
\[ 33x - 6 = 24x + 12 \]

5. **Solving for \(x\)**:
- Rearranging the equation:
\[ 33x - 24x = 12 + 6 \]
\[ 9x = 18 \]
\[ x = 2 \]

6. **Finding Kumar's Present Age**:
- Kumar's present age:
\[ 11x = 11 \times 2 = 22 \text{ years} \]

7. **Finding Kumar's Age After 6 Years**:
- Kumar's age after 6 years:
\[ 22 + 6 = 28 \text{ years} \]

### Quantity-II:

1. **Understanding the Average Age**:
- The average age of 20 students is 21 years.
- Therefore, the total age of the 20 students:
\[ 20 \times 21 = 420 \text{ years} \]

2. **Including the Teacher's Age**:
- When the teacher's age is included, the average age increases by 2 years, making it 23 years.
- The new total age with the teacher included (21 students):
\[ 23 \times 21 = 483 \text{ years} \]

3. **Finding the Teacher's Age**:
- The teacher's age can be found by subtracting the total age of the students from the new total age:
\[ 483 - 420 = 63 \text{ years} \]

4. **Finding the Teacher's Age When Joined**:
- The teacher joined 35 years ago, so:
\[ 63 - 35 = 28 \text{ years} \]

### Conclusion:

- **Quantity-I**: Kumar's age after 6 years is 28 years.
- **Quantity-II**: The teacher's age when he joined the school is also 28 years.

Thus, we find that:
- **Quantity-I = Quantity-II**.

### Final Answer:
Both quantities are equal, so the correct option is **4**.

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