Question:
In a batch of 50 students has ratio of Boys to Girls as 4:6. Average marks of Girls are 60 and Average marks of the batchis 62. Average Marks of Boys will be:
In a batch of 50 students has ratio of Boys to Girls as 4:6. Average marks of Girls are 60 and Average marks of the batchis 62. Average Marks of Boys will be:
Updated On: Dec 30, 2025
- 61
- 63
62
- 65
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The Correct Option is D
Solution and Explanation
To find the average marks of boys in the batch, we need to use the concept of weighted averages. Here are the steps to solve the problem:
- The ratio of boys to girls in the batch is given as 4:6. This implies that for every 10 students, 4 are boys and 6 are girls. Therefore, in a batch of 50 students:
- Boys = \(\frac{4}{10} \times 50 = 20\)
- Girls = \(\frac{6}{10} \times 50 = 30\)
- The average marks of the girls are given as 60. Therefore, the total marks scored by girls is:
- Total marks by girls = \(30 \times 60 = 1800\)
- The average marks of the whole batch is 62, hence the total marks for the batch is:
- Total marks of the batch = \(50 \times 62 = 3100\)
- Now, the total marks scored by the boys can be found by subtracting the total marks of the girls from the total marks of the batch:
- Total marks by boys = \(3100 - 1800 = 1300\)
- Finally, the average marks of the boys is calculated by dividing the total marks scored by boys by the number of boys:
- Average marks of boys = \(\frac{1300}{20} = 65\)
Therefore, the average marks of the boys in the batch is 65. Hence, the correct answer is 65.
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