Question

Among 680 examinees, the ratio of students passed in 1st & 2nd division is 3:5. If 34 were passed in the third division and 116 were failed, find the ratio of students passed in the first, second, & 3rd division.

A) 3:5:1
B) 5:3:1
C) 1:5:3
D) 1:3:5

Answer 1

To find the ratio of students who passed the first, second, and third divisions among 680 examinees, we take the total number of passing students and allocate them according to the given ratio of 3:5 after excluding those who passed the third division and those who failed. This calculation provides a ratio of approximately 3:5:1.

Step-by-step explanation:

The student's question asks to find the ratio of students passed in the first, second, and third divisions among 680 examinees. We know 34 students passed in the third division and 116 failed. Thus, 680 - 34 - 116 = 530 students passed in the first and second divisions. According to the given ratio of 3:5 for first and second divisions, we can divide 530 into two parts (3x and 5x). Solving the equation 3x + 5x = 530 gives us x = 530/8 = 66.25. Therefore, 3x = 3 * 66.25 = 198.75 (rounded to 199) and 5x = 5 * 66.25 = 331.25 (rounded to 331). So, the ratio of students passed in the first, second and third divisions becomes 199:331:34 which simplifies to approximately 3:5:1. Option A) 3:5:1 is therefore the correct answer.