Rs 280 are distributed into a total of 88 boys and girls .the ratio of total amount given to all the boys to that of all the girls is `4:3` .The ratio of amount given to one boy to amount given to one girl is `8:5` .Find the number of boys and girls respectively .

Options

A. A)32 and 56
B. B)36 and 52
C. C)48 and 40
D. D)40 and 48

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Understand the total distribution
We know that Rs 280 is distributed among a total of 88 boys and girls. The total amount given to boys and girls is divided in the ratio of 4:3.

### Step 2: Calculate the total units of distribution
The ratio of the total amount given to boys to that given to girls is 4:3. This means:
- Total units = 4 (for boys) + 3 (for girls) = 7 units.

### Step 3: Find the value of one unit
Since the total amount is Rs 280, we can find the value of one unit:
- Value of 1 unit = Total amount / Total units = 280 / 7 = Rs 40.

### Step 4: Calculate the amount given to boys and girls
Now we can calculate the total amount given to boys and girls:
- Amount given to boys = 4 units × Rs 40 = Rs 160.
- Amount given to girls = 3 units × Rs 40 = Rs 120.

### Step 5: Understand the ratio of amount given to one boy and one girl
The ratio of the amount given to one boy to that given to one girl is 8:5.

### Step 6: Calculate the amount received by one boy and one girl
Let the amount given to one boy be 8x and the amount given to one girl be 5x. Thus:
- Total amount given to boys = Number of boys × Amount per boy = 8x * Number of boys.
- Total amount given to girls = Number of girls × Amount per girl = 5x * Number of girls.

### Step 7: Set up equations based on the total amounts
From the amounts calculated:
- For boys: 8x * Number of boys = Rs 160
- For girls: 5x * Number of girls = Rs 120

### Step 8: Find the number of boys and girls
From the equations:
1. Number of boys = 160 / (8x) = 20/x
2. Number of girls = 120 / (5x) = 24/x

### Step 9: Use the total number of boys and girls
We know that the total number of boys and girls is 88:
- (20/x) + (24/x) = 88
- (44/x) = 88
- x = 44/88 = 0.5

### Step 10: Calculate the number of boys and girls
Now substituting x back:
- Number of boys = 20 / 0.5 = 40
- Number of girls = 24 / 0.5 = 48

### Final Answer
The number of boys is 40 and the number of girls is 48.

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