Sure, let's break down the problem step by step, given the initial conditions and the final results.
Problem Statement:
Out of 30 students in a class, two-thirds were successful in getting an A* grade in Math. Among these successful students, one-quarter got an A+ grade in science as well.
Questions:
(i) What fraction of the successful students got an A+ grade in science?
(ii) How many students were successful in getting an A+ grade in science?
(iii) How many students got a grade other than A+ in these two subjects?
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Solution:
### Step 1: Determine the number of successful students in Math
Given:
- Total number of students in the class = 30
- Fraction of students successful in Math = [tex]\( \frac{2}{3} \)[/tex]
Let's calculate the number of successful students:
[tex]\[ \text{Number of successful students} = 30 \times \frac{2}{3} = 20.0 \][/tex]
### Step 2: Determine the fraction of successful students who got an A+ grade in Science
Given:
- Among the successful students, one-quarter got an A+ grade in Science
So, the fraction of successful students who got an A+ grade in Science is [tex]\( \frac{1}{4} \)[/tex].
### Step 3: Calculate the number of successful students who got an A+ grade in Science
Using the number of successful students calculated earlier:
[tex]\[ \text{Number of successful students who got A+ in Science} = 20 \times \frac{1}{4} = 5.0 \][/tex]
### Step 4: Calculate the number of students who got other than an A+ grade in these two subjects
Now, we know:
- Total students = 30
- Students who got an A+ grade in Science = 5
Therefore, the number of students who got a grade other than an A+ in Math and Science:
[tex]\[ \text{Students with other than A+ grade} = 30 - 5 = 25.0 \][/tex]
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### Summary of Results:
(i) The fraction of the successful students who got an A+ grade in Science is [tex]\( \frac{1}{4} \)[/tex].
(ii) The number of students who were successful in getting an A+ grade in Science is 5.0.
(iii) The number of students who got a grade other than an A+ in these two subjects is 25.0.
This completes the step-by-step solution to the problem.
