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MAT Exam 2023 Paper

Question Numbers: 156-160

DIRECTIONS (Qs. 156-160): Read the information below and answer the questions that follows. There are three Colleges A, B and C. The total number of maths students in college C is 40% more than the number of science students in College A. The number of maths students in College A is 200 more than the number of maths students in College C. The number of science students in College C is equal to the average number of science and maths students in College A. The sum of the number of science students in College C and maths students in College B is equal to the number of maths students in College A. The total number of science students in all the three Colleges is 950. The total number of maths students in College B is 150.

Question : 156 of 200

Marks: +1, -0

What is the ratio of total number of science students in College C to the total number of maths students in College B?

12:5
7:2
9 : 4
8 : 3

Validate

Solution:

Concept:

Use the given relationships to find the number of science students in College C and compare it with the maths students in College B.

Explanation:

Let

S_A

and

M_A

be the science and maths students in College A.

Maths students in College B:

M_B = 150

Maths students in College C are

40\%

more than science students in A, hence

M_C = 1.4S_A

Maths students in A are 200 more than those in C, so

M_A = 1.4S_A + 200

Science students in C equal the average of science and maths students in A:

S_C = \frac{S_A + M_A}{2} = \frac{S_A + (1.4S_A + 200)}{2} = 1.2S_A + 100

Given

S_C + M_B = M_A

, substitute the values:

(1.2S_A + 100) + 150 = 1.4S_A + 200

This gives

1.2S_A + 250 = 1.4S_A + 200

, so

S_A = 250

Now

S_C = 1.2(250) + 100 = 400

Thus total science students in College C =

400

Total maths students in College B =

150

Required ratio

= 400 : 150 = 8 : 3

Answer:

8 : 3

(Option D).

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