Number of Students in Arts and Science faculties in an institute are in the ratio of 5 : 8 respectively. If 150 more students join Arts 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?
Number of Students in Arts and Science faculties in an institute are in the ratio of 5 : 8 respectively. If 150 more students join Arts 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?
A1100
B1294
C1370
D
None of these
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Correct answer is: None of these
Explanation:
Let the original number of students in Arts and Science faculties be 5x and 8x respectively.
According to the question,
\(\frac{5x+150}{8x+80} = \frac{3}{4}\)
\(\implies 24x + 240 = 20x + 600\)
\(\implies 4x = 360\)
\(\implies x= 9\)
\(\therefore \text{Original number of students = 5x + 8x = 13x}\)
\(= 13 × 90 = 1170\)
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