Latest IBM Aptitude Question SOLUTION: Three math classes: X, Y, and Z, take an algebra test. The average score in class X is 83. The average score in class Y is 76. The average score in class Z is 85. The average score

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Three math classes: X, Y, and Z, take an algebra test.
The average score in class X is 83.
The average score in class Y is 76.
The average score in class Z is 85.
The average score of all students in classes X and Y together is 79.
The average score of all students in classes Y and Z together is 81.

What is the average score for all the three classes, taken together?

Solution

According to the given condition
(83x+76y)/(x+y) = 79
on solving x = 3y/4
similarly (76y+85z)/(y+z) = 81
on solving z = 5y/4
average score for all the three classes taken together = 83x+76y+85z/x+y+z
= [83(3y/4)+85y+85(5y/4)]/[(3y/4)+y+(5y/4)]
= [(249/4)+85+(425/4)]/[(3/4)+1+(5/4)]
= [(249/4)+(340/4)+(425/4)]/[(3/4)+(4/4)+(5/4)]
= [249+340+425]/[3+4+5] = 1014/12 = 84.5

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Asked In IBM (12 years ago)

Solved Read Solution (3)

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Read Solution (3) :

kumar vikram  (11 years ago)

According to the given condition
(83x+76y)/(x+y) = 79
on solving x = 3y/4
similarly (76y+85z)/(y+z) = 81
on solving z = 5y/4
average score for all the three classes taken together = 83x+76y+85z/x+y+z

on solving you will get 978y/12y=81.5

Is this solution Helpfull? Yes (15) | No (1)  

Purbasha  (10 years ago)

Average score of class X is 83 and that of class Y is 76 and the combined average of X and Y is 79.
By rule of alligation ratio of students in X : Y is given by

X : Y

79
/

83 76

3 : 4

Similarly, average score of class Y is 76 and that of class Z is 85 and the combined average is 81.

By rule of alligation ratio of students in Y : Z is

Y : Z
81
/
76 85
4 : 5

X:Y:Z=3:4:5

Total average for X, Y and Z=(3×83+4×76+5×853+4+5)
=(249+304+425)12=81.5

Is this solution Helpfull? Yes (4) | No   

pradip mali  (6 years ago)

83+76+85=244÷3=81.33 =~ 81.5

Is this solution Helpfull? Yes (1) | No   

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