A coacching institute has students in '3' batches-X,Y, and Z.In a certain examination the average marks obtained by these batches are 72,60 and 50 respectively.The average marks of batches X and Y taken together is 69.If the ratio of the number of students in batches Y and Z is 6:7, What is the average score of all the three batches put together?64.7656258.56
Question
A coacching institute has students in '3' batches-X,Y, and Z.In a certain examination the average marks obtained by these batches are 72,60 and 50 respectively.The average marks of batches X and Y taken together is 69.If the ratio of the number of students in batches Y and Z is 6:7, What is the average score of all the three batches put together?64.7656258.56
Solution
To solve this problem, we need to use the formula for the average, which is the sum of all values divided by the number of values.
Step 1: Let's denote the number of students in batches X, Y, and Z as x, y, and z respectively.
Step 2: We know that the average marks of batches X and Y together is 69. So, we can write the equation: (72x + 60y) / (x + y) = 69.
Step 3: Simplify the equation to find the ratio of the number of students in batches X and Y. We get x/y = 9/3 = 3/1.
Step 4: We also know that the ratio of the number of students in batches Y and Z is 6:7. So, we can write y/z = 6/7.
Step 5: From steps 3 and 4, we can find the ratio of the number of students in all three batches. We get x:y:z = 18:6:7.
Step 6: The average score of all the three batches put together can be found by the formula: (72x + 60y + 50z) / (x + y + z).
Step 7: Substitute the values of x, y, and z from step 5 into the formula in step 6. We get (7218 + 606 + 50*7) / (18 + 6 + 7) = 64.76.
So, the average score of all the three batches put together is 64.76.
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