Instructions

Study the given information answer the questions that follow.

There are two coaching institutions in a town, institution A and institution B, the total number of students in both institutions are 1350. The ratio of the students in institution A to that of institution B is 7 : 8. There are only three classes in each Institution, Class X, Class Y and Class Z. In institution A, 70% students are boys and the rest are girls, whereas in institution B the ratio of boys to girls is 11 : 7.

In institution A, $$\frac{4}{7}$$ of the total girls enrolled in Class Y, $$\frac{5}{9}$$ of the remainingĀ enrolled in Class Z and rest in Class X. Out of the total boys in institution A, $$42\frac{6}{7}\%$$ enrolled in class X, $$44\frac{4}{9}\%$$ of the remaining in Class Y and the rest in Class Z.

In Institution B, $$\frac{4}{11}$$ of the total boys enrolled in class Y, and the number of boys enrolled in class Z is 5% more than the boys enrolled in class Y and rest in class X. one-fourth of the total girls are enrolled in class Z, and the number of girls enrolled in class X is 10% more than the girls enrolled in class Y.

Question 53

The number of boys enrolled in class X in institution A is what percentage more than the number of girls enrolled in class Y in institution B?

Solution

It is given thatĀ the ratio of the students in institution A to that of institution B is 7 : 8, which implies if the students in institution A is 7x, then the students in institution B is 8x.

It is also known thatĀ the total number of students in both institutions are 1350.

=> (7x+8x) = 1350 => x = 90

Thus, the students in institution A is (7*90) = 630, and the students in institution B is (8*90) = 720

It is given thatĀ In institution A, 70% students are boys and the rest are girls, whereas in institution B the ratio of boys to girls is 11 : 7.

Thus, the number of boys in institution A = (70% of 630) = 441, and the number of girls in institution A = (630-441) = 189.

Similarly, the number of boys in institution B = (11/18)*720 = 440, and the number of girls in institution B = (720-440) = 280

It is given that there are only three classes in each Institution, Class X, Class Y and Class Z.

It is known that in institution A,Ā (4/7)th of the total girls joined Class Y, which implies the total number of girls at Class Y in institution A is (4/7)*189 = 108, which implies the remaining number of girls = (189-108) = 81. It is also known that (5/9)th ofĀ the remaining girlsĀ enrolled in Class Z and rest in Class X.

Thus, the total number of girls at Class Z in institution A is (5/9)*81 = 45 =>Ā the total number of girls at Class X in institution A is (81-45) = 36

Now, in institution A, the total number of boys at Class X = (3/7)* 441 = 189, which implies the number of boys who are remaining is (441-189) = 252

It is given that (4/9) of the remaining boys are in Class Y = (4/9)*252 = 112, and the boys in class Z in institution A = (252-112) = 140

**Now, in Institution B,** (4/11)th of the boys are in Class Y = (4/11)*440 = 160, and the number of boys in Class Z is (21/20)*160 = 168, which means the number of boys in Class X = (440-160-168) = 112

Similarly, (1/4)th of the girls are in Class Z = (1/4)*280 = 70, and it is given thatĀ the number of girls enrolled in class X is 10% more than the girls enrolled in class Y.

Let the number of girls in Class Y be 100x, which implies the number of girls in Class X is 110x

Thus, (110x+100x) = 210 => x = 1 => The number of girls in Class Y is 100, and the number of girls in Class X is 110

We know that the number of boys enrolled in class X in institution A is 189, and the number of girls enrolled in class Y in institution B = 100

Thus,Ā the number of boys enrolled in class X in institution A is 89% more thanĀ the number of girls enrolled in class Y in institution B.

The correct option is B

SRCC Averages, Ratio and Proportion QuestionsSRCC Inequalities QuestionsSRCC Quadratic Equations QuestionsSRCC Profit And Loss QuestionsSRCC Averages QuestionsSRCC Time, Distance and Work QuestionsSRCC Inequalities QuestionsSRCC Probability, Combinatorics QuestionsSRCC Number Systems QuestionsSRCC Quadratic Equations QuestionsSRCC Remainders QuestionsSRCC Averages, Ratio and Proportion QuestionsSRCC Profit, Loss and Interest QuestionsSRCC Data Sufficiency QuestionsSRCC Geometry QuestionsSRCC Geometry QuestionsSRCC PGDBA Calculus QuestionsSRCC Percentages QuestionsSRCC Progressions and Series QuestionsSRCC Data Sufficiency QuestionsSRCC Linear Equations QuestionsSRCC Venn Diagrams QuestionsSRCC Logarithms, Surds and Indices QuestionsSRCC Linear Equations QuestionsSRCC Data Sufficiency QuestionsSRCC Venn Diagrams QuestionsSRCC Time And Work QuestionsSRCC Progressions and Series QuestionsSRCC Number Systems QuestionsSRCC Arithmetic QuestionsSRCC Algebra QuestionsSRCC Number Systems QuestionsSRCC Averages, Ratio and Proportion QuestionsSRCC Logarithms, Surds and Indices QuestionsSRCC Time, Distance and Work QuestionsSRCC Functions, Graphs and Statistics QuestionsSRCC Data Sufficiency QuestionsSRCC Venn Diagrams QuestionsSRCC Simple Interest Compound Interest QuestionsSRCC Venn Diagrams QuestionsSRCC Progressions and Series QuestionsSRCC Inequalities QuestionsSRCC Time Speed Distance QuestionsSRCC Number Series QuestionsSRCC Functions, Graphs and Statistics QuestionsSRCC Geometry QuestionsSRCC Probability, Combinatorics QuestionsSRCC Logarithms, Surds and Indices QuestionsSRCC Logarithms QuestionsSRCC Quadratic Equations QuestionsSRCC Quadratic Equations QuestionsSRCC Functions, Graphs and Statistics QuestionsSRCC Logarithms, Surds and Indices QuestionsSRCC Linear Equations QuestionsSRCC Averages, Ratio and Proportion QuestionsSRCC Coordinate Geometry QuestionsSRCC Time, Distance and Work QuestionsSRCC Inequalities QuestionsSRCC Probability, Combinatorics QuestionsSRCC Probability, Combinatorics QuestionsSRCC Linear Equations QuestionsSRCC Geometry QuestionsSRCC Time, Distance and Work QuestionsSRCC Progressions and Series QuestionsSRCC Profit, Loss and Interest QuestionsSRCC Number Systems QuestionsSRCC Profit, Loss and Interest QuestionsSRCC Mensuration QuestionsSRCC Functions, Graphs and Statistics QuestionsSRCC Profit, Loss and Interest QuestionsSRCC Averages Mixtures Alligations Questions

SRCC Data Interpretation QuestionsSRCC Scheduling QuestionsSRCC Special Charts QuestionsSRCC Quant Based LR QuestionsSRCC Charts QuestionsSRCC Quant Based DI QuestionsSRCC Logical Reasoning QuestionsSRCC Scheduling QuestionsSRCC DI Miscellaneous QuestionsSRCC Truth Lie Concept QuestionsSRCC 2D & 3D LR QuestionsSRCC Data Interpretation Basics QuestionsSRCC Coins and Weights QuestionsSRCC Miscellaneous LR QuestionsSRCC Arrangement QuestionsSRCC Routes And Networks QuestionsSRCC Data Interpretation QuestionsSRCC Logical Reasoning QuestionsSRCC Charts QuestionsSRCC Games and Tournamnents QuestionsSRCC Maxima-Minima QuestionsSRCC Selection With Condition QuestionsSRCC Table with Missing values QuestionsSRCC Games and Tournamnents QuestionsSRCC DI with connected data sets QuestionsSRCC Logical Reasoning QuestionsSRCC Data Interpretation Basics QuestionsSRCC Charts QuestionsSRCC Puzzles QuestionsSRCC DI with connected data sets QuestionsSRCC Innovation and Entrepreneurship QuestionsSRCC Truth Lie Concept QuestionsSRCC Data change over a period QuestionsSRCC Puzzles QuestionsSRCC Data Interpretation QuestionsSRCC Data Interpretation Basics QuestionsSRCC Arrangement QuestionsSRCC Set Theory QuestionsSRCC Selection With Condition QuestionsSRCC Data change over a period QuestionsSRCC Venn Diagrams QuestionsSRCC Quant Based LR QuestionsSRCC Data Interpretation QuestionsSRCC Table with Missing values QuestionsSRCC Arrangement QuestionsSRCC Special Charts QuestionsSRCC Quant Based DI Questions

SRCC Verbal Ability QuestionsSRCC Grammar and Sentence Correction QuestionsSRCC Vocabulary QuestionsSRCC Critical Reasoning QuestionsSRCC Vocabulary QuestionsSRCC Grammar and Sentence Correction QuestionsSRCC Reading Comprehension QuestionsSRCC Reading Comprehension QuestionsSRCC Critical Reasoning QuestionsSRCC Para Summary QuestionsSRCC Miscellaneous QuestionsSRCC Grammar and Sentence Correction QuestionsSRCC Para Jumbles QuestionsSRCC Vocabulary QuestionsSRCC Reading Comprehension QuestionsSRCC Para Jumbles QuestionsSRCC Grammar and Sentence Correction QuestionsSRCC Para Summary QuestionsSRCC Reading Comprehension QuestionsSRCC Vocabulary QuestionsSRCC Miscellaneous QuestionsSRCC Para Jumbles QuestionsSRCC Para Jumbles QuestionsSRCC Critical Reasoning QuestionsSRCC Odd One Out QuestionsSRCC Para Summary Questions