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 56

The total number of boys enrolled in classes X and Y in institution A is what percentage of the total number of girls enrolled in classes Y and Z in institution B (rounded off to the integer)?

Solution

It is given that 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 that 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 that 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, (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 of the remaining girls 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 => 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 that 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

Hence, theĀ total number of boys enrolled in classes X and Y in institution A = (189+112) = 301, and the numberĀ of girls enrolled in classes Y and Z in institution B = (100+70) = 170

Therefore, theĀ total number of boys enrolled in classes X and Y in institution A is (301/170)*100% = 177%

The correct option is A

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