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Chapter 18: Problem 734

The average marks of boys in a class is 50 and that of girls is 40 . The average marks of boys and girls combined is 48 . The percentage of boys in the class is (a) 75 (b) 80 (c) 60 (d) 55

Short Answer

Expert verified
The percentage of boys in the class is 80% (b).

Step by step solution

01

Understand the given information

We are given the following information: - The average marks of boys in a class is 50 - The average marks of girls in a class is 40 - The average marks of the entire class (boys and girls combined) is 48 We need to find the percentage of boys in the class.
02

Set up the weighted average equation

Let the number of boys in the class be b and the number of girls be g. The total number of students in the class is b+g. We are given the average marks of boys is 50, so the total marks of boys = 50b. Similarly, the average marks of girls are 40, so the total marks of girls = 40g. Average marks of the entire class = 48, which means the total marks of the entire class are 48(b+g). Now, we can set up the equation for weighted averages: Total marks of boys + Total marks of girls = Total marks of the entire class So, 50b + 40g = 48(b+g)
03

Solve the equation to find the ratio of boys to girls

We need to solve the equation 50b + 40g = 48(b+g) to find the ratio of boys to girls: Expanding the equation, we get: 50b + 40g = 48b + 48g Simplifying the equation, we get: 2b = 8g Further simplification gives us the ratio: b:g = 4:1
04

Calculate the percentage of boys in the class

We have found that the ratio of boys to girls in the class is 4:1. To find the percentage of boys in the class, we can use the formula: Percentage of boys = (Number of boys / Total number of students) × 100 The total number of students in the class can be found by adding the numbers in the ratio: Total number of students = 4 (from boys) + 1 (from girls) = 5 Now, we can find the percentage of boys in the class: Percentage of boys = (4/5) × 100 = 80% Therefore, the right answer is (b) 80.

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Most popular questions from this chapter

A dice is tossed until 1 comes. Then the probability that 1 comes in even number of trials is (a) \((5 / 11)\) (b) \((5 / 6)\) (c) \((6 / 11)\) (d) \((1 / 6)\)

A dice is rolled three times, the probability of getting a larger number than the previous number is (a) \((6 / 216)\) (b) \((5 / 54)\) (c) \((1 / 6)\) (d) \((7 / 36)\)

Variance of \(1,3,5,7 \ldots \ldots \ldots(4 n+1)\) is (a) \([\\{2 n(2 n-1)\\} / 3]\) (c) \((1 / n) \sqrt\left[\left(n^{2}-1\right) / 3\right] 100\) (d) \([\\{4 n(n+1)\\} / 3]\)

Standard deviation of two observations is \(3.5\), one observation is 3 then second observation is (a) 9 (b) 10 (c) 7 (d) 3

If \(\quad 10 \Sigma_{i=1}(x i-8)=9\) and \({ }^{10} \sum_{i=1}(x i-8)^{2}=45\) then standard deviation of \(\mathrm{x}_{1}, \mathrm{x}_{2}, \mathrm{x}_{3} \ldots \ldots \ldots \mathrm{x}_{10}\) is (a) \(19.2\) (b) \(12.92\) (c) \(1.82\) (d) \(1.92\)
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