A sum of Rs. 41 was divided among 50 boys and girls. Each boy gets 90 paise and a girl 65 paise. Find the ratio of number of boys and girls :

Question

Accepted Answer

To solve the problem of finding the ratio of the number of boys to girls, we need to use the information provided:

1. The total sum of money distributed is Rs. 41, which is equivalent to 4100 paise (since 1 Rupee = 100 paise).
2. Each boy receives 90 paise.
3. Each girl receives 65 paise.
4. The total number of boys and girls is 50.

Let's denote the number of boys as $ b $ and the number of girls as $ g $.

From the problem, we have two equations:

1. The total number of boys and girls is 50:
   $$
   b + g = 50
   $$

2. The total amount of money distributed is 4100 paise:
   $$
   90b + 65g = 4100
   $$

Now, let's solve these equations to find the values of $ b $ and $ g $.

First, solve the first equation for $ g $:
$$
g = 50 - b
$$

Substitute $ g = 50 - b $ into the second equation:
$$
90b + 65(50 - b) = 4100
$$

Simplify and solve for $ b $:
$$
90b + 3250 - 65b = 4100
$$
$$
25b + 3250 = 4100
$$
$$
25b = 4100 - 3250
$$
$$
25b = 850
$$
$$
b = \frac{850}{25}
$$
$$
b = 34
$$

Now, substitute $ b = 34 $ back into the equation for $ g $:
$$
g = 50 - 34
$$
$$
g = 16
$$

Thus, the number of boys is 34 and the number of girls is 16. The ratio of the number of boys to girls is:
$$
\frac{b}{g} = \frac{34}{16} = \frac{17}{8}
$$

Therefore, the correct ratio of the number of boys to girls is 17:8, which corresponds to Option 2.

**Explanation of why other options are incorrect:**

- **Option 1 and Option 4**: These options are not numerical ratios but rather appear to be incorrectly formatted date-time strings. They do not represent a valid ratio of boys to girls and are irrelevant to the context of the problem.
  
- **Option 3 (13:8)**: This ratio does not satisfy the conditions set by the problem. If we assume 13 boys and 8 girls, the total number of students would not be 50, and the distribution of money would not add up to 4100 paise. Therefore, this option is incorrect.

In conclusion, Option 2 (17:8) is the correct answer, as it accurately represents the ratio of the number of boys to girls based on the given conditions.