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The average weight of a group of 14 boys was was the number of boys in the another group? 48 kg When another group of boys having gan average weight of 51 kg yoned thest ther new average wegt

(A) 14

(8) 12

(C) 10

(D) 7

To solve this problem, we need to use the concept of averages and weighted averages.

### Let's break down the problem:

1. **Group 1 (14 boys):**
   - Number of boys = 14
   - Average weight = 48 kg

2. **Group 2 (Number of boys = \( x \)):**
   - Average weight = 51 kg

3. **Combined Group:**
   - The average weight after combining both groups = 49 kg

### Steps to Solve:

1. **Total weight of Group 1:**
   \[
   \text{Total weight of Group 1} = 14 \times 48 = 672 \text{ kg}
   \]

2. **Total weight of Group 2:**
   \[
   \text{Total weight of Group 2} = 51x \text{ kg}
   \]

3. **Total number of boys in the combined group:**
   \[
   14 + x
   \]

4. **Total weight of the combined group:**
   \[
   672 + 51x \text{ kg}
   \]

5. **Given the average weight of the combined group:**
   \[
   \frac{672 + 51x}{14 + x} = 49
   \]

6. **Solve for \( x \):**

   Multiply both sides by \( 14 + x \) to eliminate the denominator:
   \[
   672 + 51x = 49(14 + x)
   \]

   Distribute 49 on the right side:
   \[
   672 + 51x = 686 + 49x
   \]

   Move all terms involving \( x \) to one side and constants to the other:
   \[
   51x - 49x = 686 - 672
   \]
   \[
   2x = 14
   \]

   Solve for \( x \):
   \[
   x = \frac{14}{2} = 7
   \]

### Answer:
The number of boys in the second group is **7**.

The correct option is **(D) 7**.

---

Would you like further details on this solution, or do you have any other questions?

Here are five related questions you might find interesting:

1. How would the average change if Group 2 had an average weight of 52 kg?
2. What would be the average weight if the number of boys in Group 2 was 10 instead of 7?
3. Can you find the total weight of the combined group?
4. How would the solution change if the average weight of the combined group was 50 kg instead of 49 kg?
5. What happens if the average weight of Group 1 changes to 50 kg?

**Tip:** When solving problems involving averages and weighted averages, always start by calculating the total sums involved before combining them to find the new average.

Learn how to calculate the average weight of boys in two groups using the concept of averages and weighted averages. Solve a problem involving two groups of boys with different average weights and find out the number of boys in the second group. Suitable for Grades 7-9.

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