GATE CS 2021 Set 2 — Question 8
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General Aptitude → Quantitative Aptitude → Ratios, Percentages, Powers, Exponents & Logarithms
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Question
The number of students in three classes is in the ratio 3:13:6. If 18 students are added to each class, the ratio changes to 15:35:21.The total number of students in all the three classes in the beginning was:
Correct answer
(C) 88
Solution
Let the number of students in the three classes be , , and respectively.
Total number of students initially = .According to the problem, 18 students are added to each class. The new number of students becomes:
, , and .The new ratio is given as .
We can set up an equation using the ratio of the first two classes:Simplify the fraction by dividing numerator and denominator by 5:Cross-multiply:Now, substitute into the expression for the total number of students initially:
Total students = .We can verify with the third class ratio:
Class 1:
Class 2:
Class 3:
Ratio: . Dividing by 2 gives , which matches the given ratio.Thus, the initial total number of students was 88.
Total number of students initially = .According to the problem, 18 students are added to each class. The new number of students becomes:
, , and .The new ratio is given as .
We can set up an equation using the ratio of the first two classes:Simplify the fraction by dividing numerator and denominator by 5:Cross-multiply:Now, substitute into the expression for the total number of students initially:
Total students = .We can verify with the third class ratio:
Class 1:
Class 2:
Class 3:
Ratio: . Dividing by 2 gives , which matches the given ratio.Thus, the initial total number of students was 88.
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