In a class, there are 60% female students and the remaining are male. 40% of the female students and 70% of the male students have opted for the research methodology course. If in all, 60 students have not opted for the research methdology course, which of the following is the total number of students in the class?
125
Let's solve this problem step-by-step to find the total number of students in the class.
- Let the total number of students in the class be \(x\).
- According to the problem, 60% of the students are female. Thus, the number of female students is \(0.6x\).
- The remaining students are male, which makes up 40% of the class. Therefore, the number of male students is \(0.4x\).
Next, let's explore who opted for the research methodology course:
- 40% of the female students have opted for the research methodology course.
- Thus, the number of female students who opted for the course is \(0.4 \times 0.6x = 0.24x\).
- 70% of the male students have opted for the research methodology course.
- Thus, the number of male students who opted for the course is \(0.7 \times 0.4x = 0.28x\).
The problem states a certain number of students have not opted for the course:
- The total number of students who opted for the course is the sum of females and males who opted: \(0.24x + 0.28x = 0.52x\).
- Therefore, the number of students who have not opted for the research methodology course is: \(x - 0.52x = 0.48x\).
- According to the problem, this number is 60. Hence, we have the equation: \(0.48x = 60\).
- Solving for \(x\) gives: \(x = \frac{60}{0.48} = 125\).
Thus, the total number of students in the class is 125.
Let's verify our answer by checking the calculation:
- Number of female students = \(0.6 \times 125 = 75\)
- Number of male students = \(0.4 \times 125 = 50\)
- Females opted for the course = \(40\% \times 75 = 30\)
- Males opted for the course = \(70\% \times 50 = 35\)
- Total students opted = \(30 + 35 = 65\)
- Students not opted = \(125 - 65 = 60\) (matches given)
Therefore, the computations confirm that the total number of students is indeed 125, matching the given condition.
Similar Questions
If the price of sugar increases by 25%, determine the percentage by which its consumption be reduced so as not to increase the expenditure on it?
If 3% of (a + b) = 7% of (ab)
and 5 % of (a − b) = 4% of (ab),
then what percentage of b is a?The length of the side of a square (5.0 cm × 5.0 cm) is increased by 1%. By what percentage (%) the area of the square increases?
If 60% of (a − b) = 40% of (a + b), then what percent of a is b?
Manoj's commission is 10% on all sales up to Rs. 10,000 and 5% on all sales exceeding this. He remits Rs. 75,500 to his company after deducting his commission. The total sales will come out to be:
If x and y are two positive numbers and x is 25% greater than y, what is the value of the ratio y/x?
5% of the inhabitants of a village having died of malaria, a panic set in. During this, 20% of the remaining inhabitants left the village. The population is then reduced to 4750. Find the number of original inhabitants?
In a class, 20% of the boys have blue eyes and 10% of the girls have blue eyes. If the ratio of boys to girls in the class is 4:3, then what is the portion of the students in the class having blue eyes?
During one year, the population of a town increased by 5% and during the next year, the population decreased by 5%. If the total population is 29925 at the end of the second year, then what was the population size in the beginning of the first year?
In a new budget, the price of petrol rose by 25%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase?
Important Questions from Percentage
In an examination, 25% of the candidates failed in Mathematics and 12% failed in English. If 10% of the candidates failed in both the subjects and 292 candidates passed in both the subjects, which one of the following is the number of total candidates appeared in the examination?
What is the value of 9% of 5500 + 2.4% of 1100 - 40% of 1600?
Population of a village is 7960 in which 4660 are female. If in that village 60% are literate in which 70% female are literate, then what is the number of literate male ?
The numbers of students of three classes of a school are in the ratio 4 : 5 : 6. If numbers of students in these classes increase by 25%, 20% and 25% respectively, then ratio of numbers of students will become:
In an examination, Ram obtained 20 % more than Ashok but 10% less than Rajesh. If the marks obtained by Ashok is 1080. Then the Percentage marks obtained by Rajesh if the full marks is 2000 ;
