In a game of 80 points, A can give 10 points to B and 20 points to C.Then, how many points can B give C in a game of 70 points?

Options

A. (1) 20
B. (2) 30
C. (3) 40
D. (4) 10

Answer

To solve the problem step by step, we need to determine how many points B can give C in a game of 70 points, based on the information provided about A, B, and C in a game of 80 points.

### Step 1: Understand the Given Information
In a game of 80 points:
- A can give 10 points to B.
- A can give 20 points to C.

This means:
- If A scores 80 points, B scores 70 points (80 - 10).
- If A scores 80 points, C scores 60 points (80 - 20).

### Step 2: Establish Ratios
From the above information, we can establish the following ratios:
- The ratio of A to B (A:B) is 80:70, which simplifies to 8:7.
- The ratio of A to C (A:C) is 80:60, which simplifies to 8:6.

### Step 3: Combine the Ratios
Now we can combine these ratios to find the ratio of B to C. We already have:
- A:B = 8:7
- A:C = 8:6

To find the ratio of B to C, we can express both ratios in terms of A:
- Let A = 8k (for some k).
- Then B = 7k and C = 6k.

### Step 4: Find the Difference Between B and C
Now we find the difference between B and C:
- B - C = 7k - 6k = k.

### Step 5: Set Up the Game of 70 Points
In a game of 70 points, we need to find how many points B can give to C. The ratio of B to C remains the same, so we can express it as:
- B:C = 7:6.

### Step 6: Calculate Points in a Game of 70
Now, we need to find how many points B can give to C in a game of 70 points:
- Total parts in the ratio = 7 + 6 = 13 parts.
- Each part = 70 / 13 = 5.38 (approximately).

### Step 7: Calculate Points Given by B to C
Now we can calculate the points:
- Points B would score = 7 parts = 7 * 5.38 = 37.66 (approximately).
- Points C would score = 6 parts = 6 * 5.38 = 32.28 (approximately).

### Step 8: Calculate the Difference
Now we find the difference between B's and C's scores:
- Difference = B's score - C's score = 37.66 - 32.28 = 5.38.

Since we are looking for whole points, we can round this to the nearest whole number, which gives us approximately 5 points.

### Final Answer
Thus, B can give C approximately **5 points** in a game of 70 points.

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