In X's opinion, his weightis greater than 60 kg butless than 68 kg, Y doesn't agree with him and says that X's weightis more than 62 kg but less than 70 kg. The mother of X believes that the weight of X is greater than 64 kg.If all of them are correctin their estimation, then whatis the average of different probable weights ofX. ifthe weightis in integer?

Options

A. 68 kg
B. 67 kg
C. 66 kg
D. 65 kg

Answer

To solve the problem step by step, let's analyze the information given and find the common probable weights for X.

### Step 1: Analyze X's Opinion
X believes that his weight is:
- Greater than 60 kg
- Less than 68 kg

This can be expressed as:
\[ 60 < X < 68 \]

### Step 2: Determine Possible Values from X's Opinion
The integer values that satisfy this inequality are:
- 61, 62, 63, 64, 65, 66, 67

### Step 3: Analyze Y's Opinion
Y disagrees and states that X's weight is:
- Greater than 62 kg
- Less than 70 kg

This can be expressed as:
\[ 62 < X < 70 \]

### Step 4: Determine Possible Values from Y's Opinion
The integer values that satisfy this inequality are:
- 63, 64, 65, 66, 67, 68, 69

### Step 5: Analyze X's Mother's Opinion
X's mother believes that X's weight is:
- Greater than 64 kg

This can be expressed as:
\[ X > 64 \]

### Step 6: Determine Possible Values from X's Mother's Opinion
The integer values that satisfy this inequality are:
- 65, 66, 67, 68, 69, ...

### Step 7: Find Common Values
Now, we need to find the common integer values that satisfy all three opinions:
1. From X: 61, 62, 63, 64, 65, 66, 67
2. From Y: 63, 64, 65, 66, 67, 68, 69
3. From X's Mother: 65, 66, 67, 68, 69, ...

The common values from all three sets are:
- 65, 66, 67

### Step 8: Calculate the Average
To find the average of the common probable weights:
1. Sum the values: \( 65 + 66 + 67 = 198 \)
2. Count the number of values: There are 3 values (65, 66, 67).
3. Calculate the average:
\[ \text{Average} = \frac{\text{Sum of values}}{\text{Number of values}} = \frac{198}{3} = 66 \]

### Conclusion
The average of the different probable weights of X is **66 kg**.

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