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Out of 1000 student 658 failed in the aggregate, 166 in the aggregate and in group-I 434 in aggregate and in group-II, 372 in group-I, 590 in group-II and 126 in both the groups. How many failed in group-II but not in group-I?
- a)106
- b)224
- c)206
- d)464
Correct answer is option 'D'. Can you explain this answer?
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Out of 1000 student 658 failed in the aggregate, 166 in the aggregate ...
Given information:
- Total students = 1000
- Students failed in aggregate = 658
- Students failed in group-I only = 372
- Students failed in group-II only = ?
- Students failed in both groups = 126
- Students failed in aggregate and group-I = 434
- Students failed in aggregate and group-II = 166
Finding the number of students who failed in group-II but not in group-I:
Let's start by finding the total number of students who failed in group-II, including those who failed in both groups.
Total students who failed in group-II = Students failed in aggregate and group-II + Students failed in group-II only
= 166 + x (let x be the number of students who failed in group-II only)
We also know that the total number of students who failed in aggregate is 658, and out of those, 434 also failed in group-I. So the number of students who failed in aggregate but not in group-I is:
Students failed in aggregate but not in group-I = Total students who failed in aggregate - Students failed in aggregate and group-I
= 658 - 434
= 224
Now we can use this information to find the value of x.
Students failed in group-II only = Total students who failed in group-II - Students failed in both groups - Students failed in aggregate but not in group-I
= (166 + x) - 126 - 224
= x - 184
We know that the total number of students who failed in group-II only and not in group-I is x - 184. We want to find the value of x that satisfies this condition. We also know that the total number of students who failed in group-I only is 372. Therefore, we can write the following equation:
Total students who failed in group-II only and not in group-I = Total students who failed in group-II only - Students failed in both groups
x - 184 = (Total students who failed in group-II) - 126
Substituting the expression we derived for the total students who failed in group-II, we get:
x - 184 = (166 + x) - 126
x - 184 = x + 40
184 = 40
This is clearly a contradiction, which means there is no value of x that satisfies the original condition. Therefore, the answer is none of the above.
- Total students = 1000
- Students failed in aggregate = 658
- Students failed in group-I only = 372
- Students failed in group-II only = ?
- Students failed in both groups = 126
- Students failed in aggregate and group-I = 434
- Students failed in aggregate and group-II = 166
Finding the number of students who failed in group-II but not in group-I:
Let's start by finding the total number of students who failed in group-II, including those who failed in both groups.
Total students who failed in group-II = Students failed in aggregate and group-II + Students failed in group-II only
= 166 + x (let x be the number of students who failed in group-II only)
We also know that the total number of students who failed in aggregate is 658, and out of those, 434 also failed in group-I. So the number of students who failed in aggregate but not in group-I is:
Students failed in aggregate but not in group-I = Total students who failed in aggregate - Students failed in aggregate and group-I
= 658 - 434
= 224
Now we can use this information to find the value of x.
Students failed in group-II only = Total students who failed in group-II - Students failed in both groups - Students failed in aggregate but not in group-I
= (166 + x) - 126 - 224
= x - 184
We know that the total number of students who failed in group-II only and not in group-I is x - 184. We want to find the value of x that satisfies this condition. We also know that the total number of students who failed in group-I only is 372. Therefore, we can write the following equation:
Total students who failed in group-II only and not in group-I = Total students who failed in group-II only - Students failed in both groups
x - 184 = (Total students who failed in group-II) - 126
Substituting the expression we derived for the total students who failed in group-II, we get:
x - 184 = (166 + x) - 126
x - 184 = x + 40
184 = 40
This is clearly a contradiction, which means there is no value of x that satisfies the original condition. Therefore, the answer is none of the above.
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