There are two houses in parliament. One is lok sabha and the other one is rajya sabha and the member of parliaments (mps) in both the houses in 300 and 200 respectively. The average age of the member of lok sabha and rajya sabha is 40 years and 50 years respectively. A member of rajay sabha and becomes the members of the lok sabha. thus the average age of both the houses increases which one of the following statements is true/

Options

A. The age of this member is greather than 50 years
B. The age of this member is less than 40 years
C. The age of this member is greater than 40 but less than 50 years
D. none of the above

Answer

To solve the problem step by step, we will calculate the average ages and analyze the situation when a member from Rajya Sabha moves to Lok Sabha.

### Step 1: Calculate the total age of members in Lok Sabha and Rajya Sabha.

1. **Total members in Lok Sabha (L)** = 300
2. **Average age of members in Lok Sabha** = 40 years
3. **Total age of members in Lok Sabha** = Total members × Average age = 300 × 40 = **12000 years**

4. **Total members in Rajya Sabha (R)** = 200
5. **Average age of members in Rajya Sabha** = 50 years
6. **Total age of members in Rajya Sabha** = Total members × Average age = 200 × 50 = **10000 years**

### Step 2: Analyze the situation when a member from Rajya Sabha moves to Lok Sabha.

1. Let the age of the member moving from Rajya Sabha to Lok Sabha be **x** years.
2. After this member moves:
- New total members in Lok Sabha = 300 + 1 = **301**
- New total age in Lok Sabha = 12000 + x
- New average age in Lok Sabha = (12000 + x) / 301

3. For Rajya Sabha:
- New total members in Rajya Sabha = 200 - 1 = **199**
- New total age in Rajya Sabha = 10000 - x
- New average age in Rajya Sabha = (10000 - x) / 199

### Step 3: Determine the conditions for the average ages to increase.

1. For the average age of Lok Sabha to increase:
- (12000 + x) / 301 > 40
- This simplifies to: 12000 + x > 12040
- Therefore, x > 40

2. For the average age of Rajya Sabha to decrease:
- (10000 - x) / 199 < 50
- This simplifies to: 10000 - x < 9950
- Therefore, x > 50

### Conclusion:

From the above conditions, we find that:
- The age of the member (x) must be greater than 40 for Lok Sabha's average to increase.
- The age of the member (x) must be greater than 50 for Rajya Sabha's average to decrease.

Thus, the age of the member moving from Rajya Sabha to Lok Sabha must be greater than 40 but less than 50, which is not possible. Therefore, the only valid conclusion is that the age of the member must be greater than 40 and less than 50.

### Final Answer:
The age of the member who moved from Rajya Sabha to Lok Sabha is greater than 40 but less than 50.

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