| 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] |
A) 1200
B) 1400
C) 1150
D) Cannot be determined
E) None of the above
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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