Analyzing Education Budget Allocation for State P in 2021

The question asks us to determine the amount of money spent on higher education for boys in State P in the year 2021, based on the provided budget allocation table and specific spending details.

Extracting Relevant Data

First, let's look at the budget allocation for State P in 2021 from the table:

From the table, the total budget allocated for education in State P in 2021 was Rs. 410 crore.

Calculating Spending on Boys' Education

The question states that State P spent three-fourth of the allocated budget on boys in 2021.

Amount spent on boys = $\text{Total allocated budget} \times \frac{3}{4}$

Amount spent on boys = $\text{Rs. } 410 \times \frac{3}{4}$

Amount spent on boys = $\text{Rs. } \frac{1230}{4}$

Amount spent on boys = $\text{Rs. } 307.5 \text{ crore}$.

Calculating Spending on Higher Education for Boys

The money spent on school education and higher education of boys was in the ratio 20 : 21.

Let the amount spent on school education of boys be $20x$ and the amount spent on higher education of boys be $21x$.

The total amount spent on boys is the sum of spending on school and higher education for boys:

Total amount spent on boys = Amount on school education + Amount on higher education

$\text{Rs. } 307.5 \text{ crore} = 20x + 21x$

$\text{Rs. } 307.5 \text{ crore} = 41x$

To find the value of $x$, we divide the total amount by the sum of the ratio parts:

$x = \frac{307.5}{41}$

$x = 7.5$

Now, we can find the amount spent on higher education of boys, which is $21x$:

Amount spent on higher education of boys = $21 \times x$

Amount spent on higher education of boys = $21 \times 7.5$

Amount spent on higher education of boys = $157.5$

So, Rs. 157.5 crore was spent on higher education of boys.

Step-by-Step Calculation Summary

1. Identify the total budget allocation for State P in 2021: Rs. 410 crore.
2. Calculate the total amount spent on boys: $\frac{3}{4} \times 410 = 307.5$ crore.
3. Understand the ratio of spending on school vs. higher education for boys: 20:21.
4. The total ratio parts are $20 + 21 = 41$.
5. The fraction of the total amount spent on boys that goes to higher education is $\frac{21}{41}$.
6. Calculate the amount spent on higher education for boys: $\frac{21}{41} \times 307.5 = 157.5$ crore.

The amount spent on higher education of boys in State P in 2021 is Rs. 157.5 crore.

Revision Table: Key Education Budget Concepts

Additional Information: Analyzing Budget Ratios

When a total amount is divided according to a given ratio, say A : B, the total number of parts is A + B. The fraction of the total corresponding to A is $\frac{A}{A+B}$, and the fraction corresponding to B is $\frac{B}{A+B}$. To find the actual amount for each part, you multiply the total amount by the respective fraction.

In this problem, the total amount spent on boys (Rs. 307.5 crore) was divided in the ratio 20:21 for school and higher education. The total ratio parts are 41. The fraction for higher education is $\frac{21}{41}$. Therefore, the amount for higher education is $\frac{21}{41} \times \text{Rs. } 307.5 \text{ crore}$. This method is fundamental in solving problems involving distribution based on ratios.