SATHEE: Quantitative Aptitude Ques 824

Quantitative Aptitude Ques 824

Question: Number of students in Arts and Science faculties in an institute are in the ratio of 5: 8, respectively. If 150 more students join Art faculty while 80 more students join Science faculty, the respective ratio becomes 3: 4. Originally, what was the total number of students in both faculties together? [PNB (SO) 2009]

Options:

A) 1200

B) 1400

C) 1150

D) Cannot be determined

E) None of the above

Show Answer

Answer:

Correct Answer: E

Solution:

Let the original number of students in Arts and Science faculties by 5x and 8x, respectively. According to the question, $ \frac{5x+150}{8x+80}=\frac{4}{3} $

$ \Rightarrow $ $ 24x+240=20x+600 $

$ \Rightarrow $ $ 4x=360 $

$ \Rightarrow $ $ x=\frac{360}{4}=90 $

$ \therefore $ Original number of students $ =5x+8x=13x $ $ =13\times 90=1170 $

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