Calculating Successful Student Ratios in BCA Program

This problem asks us to find the ratio of boys to girls who have successfully completed the B.C.A. program, given the overall ratio of boys to girls in that program and their respective success percentages.

Understanding the Given Data

We are provided with the following information for the B.C.A. program:

• Percentage of successful boys in B.C.A.: 70%
• Percentage of successful girls in B.C.A.: 80%
• Ratio of the total number of boys to the total number of girls in B.C.A.: 4 : 1

Setting up the Calculation

Let's assume the total number of boys in the B.C.A. program is $4x$ and the total number of girls in the B.C.A. program is $1x$ (or simply $x$), based on the given ratio of 4 : 1. Here, $x$ is a positive number representing a common multiplier.

Calculating the Number of Successful Boys

The number of boys who successfully completed the B.C.A. program is 70% of the total number of boys.
Number of successful boys $= 70\% \text{ of } 4x$
Number of successful boys $= \frac{70}{100} \times 4x$
Number of successful boys $= 0.70 \times 4x$
Number of successful boys $= 2.8x$

Calculating the Number of Successful Girls

The number of girls who successfully completed the B.C.A. program is 80% of the total number of girls.
Number of successful girls $= 80\% \text{ of } x$
Number of successful girls $= \frac{80}{100} \times x$
Number of successful girls $= 0.80 \times x$
Number of successful girls $= 0.8x$

Determining the Ratio of Successful Students

Now we need to find the ratio of the number of boys who successfully completed B.C.A. to the number of girls who successfully completed B.C.A.

Ratio $= (\text{Number of successful boys}) : (\text{Number of successful girls})$
Ratio $= 2.8x : 0.8x$

To simplify the ratio, we can divide both sides by $x$ (since $x$ is a positive number):
Ratio $= 2.8 : 0.8$

To remove the decimals, we can multiply both sides by 10:
Ratio $= 2.8 \times 10 : 0.8 \times 10$
Ratio $= 28 : 8$

Now, we can simplify the ratio by dividing both numbers by their greatest common divisor, which is 4:
Ratio $= \frac{28}{4} : \frac{8}{4}$
Ratio $= 7 : 2$

So, the ratio between the number of boys who have successfully completed B.C.A. to the number of girls who have successfully completed B.C.A. is 7 : 2.

Conclusion

Based on the calculations, the ratio of successful boys to successful girls in the B.C.A. program is 7 : 2.

Revision Table: BCA Success Ratio

Additional Information: Working with Ratios and Percentages

When dealing with problems involving ratios and percentages, it's often helpful to represent the quantities using a variable (like $x$) to maintain the given ratio. Percentages are converted to decimals or fractions before performing calculations.

• A ratio like $a:b$ means that for every $a$ units of the first quantity, there are $b$ units of the second. The total quantity can be considered as $(a+b)$ units.
• To convert a percentage to a decimal, divide by 100. For example, 70% is $70/100 = 0.70$.
• When calculating a percentage of a quantity, multiply the decimal form of the percentage by the quantity.
• Ratios can be simplified by dividing both parts by their greatest common divisor. Multiplying or dividing both parts of a ratio by the same non-zero number does not change the ratio's value.