A student gets an aggregate of 60% marks in five subjects, in the ratio 10 : 9 : 8 : 7 : 6. The pass marks is 50% of the maximum marks for all the subjects. If each subject has the same maximum marks, in how many subjects did he pass the examination?radio_button_unchecked2radio_button_unchecked3radio_button_unchecked4radio_button_uncheckedCannot be determined
Question
A student gets an aggregate of 60% marks in five subjects, in the ratio 10 : 9 : 8 : 7 : 6. The pass marks is 50% of the maximum marks for all the subjects. If each subject has the same maximum marks, in how many subjects did he pass the examination?radio_button_unchecked2radio_button_unchecked3radio_button_unchecked4radio_button_uncheckedCannot be determined
Solution
The problem states that the student's marks are distributed in the ratio 10:9:8:7:6 across five subjects. This means that if we add up these ratios, we get a total of 40 parts.
The student's aggregate mark is 60%. The pass mark for each subject is 50%.
Let's assume that the maximum marks for each subject is 100 (since percentages are based on a maximum of 100). This means that the pass mark for each subject is 50 marks.
Now, let's find out how many marks the student got in each subject.
The student's total marks are 60% of the total maximum marks. Since there are five subjects, the total maximum marks are 5 * 100 = 500. So, the student's total marks are 60% of 500 = 300 marks.
Since the total of 300 marks is distributed in the ratio 10:9:8:7:6, we can find out the marks in each subject by dividing 300 by the total number of parts (which is 40) and then multiplying by the number of parts for each subject.
So, the marks in each subject are:
- Subject 1: (300/40) * 10 = 75 marks
- Subject 2: (300/40) * 9 = 67.5 marks
- Subject 3: (300/40) * 8 = 60 marks
- Subject 4: (300/40) * 7 = 52.5 marks
- Subject 5: (300/40) * 6 = 45 marks
Now, we can see that the student has passed in the first four subjects (since he got more than 50 marks in each), but failed in the fifth subject (since he got less than 50 marks).
So, the student passed in 4 subjects.
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