Question

Number of students in Arts and Science 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?
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Answer 1

Answer:

• The total number of students in both faculties together = 1170 students

Step-by-step explanation:

Given that:

• Number of students in Arts and Science are in the ratio of 5 : 8 respectively.
• 150 more students join Arts faculty while 80 more students join science faculty.
• The respective ratio becomes 3 : 4.

Let us assume:

• The number of students in Arts and Science be 5x and 8x respectively.

Finding the number of students:

→ (5x + 150)/(8x + 80) = 3/4

→ 4(5x + 150) = 3(8x + 80)

→ 20x + 600 = 24x + 240

→ 24x - 20x = 600 - 240

→ 4x = 360

→ x = 360/4

→ x = 90

Number of students:

• Arts students = 5x = (5 × 90) = 450
• Science students = 8x = (8 × 90) = 720

Finding the total number of students:

→ Total students = Arts students + Science students

→ Total students = 450 + 720

→ Total students = 1170

Answer 2

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Number of students in Arts and Science 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?

${\huge{\boxed{\frak{\underline{\underline{Answer:}}}}}}$

Let,

• Number of students in art = 5x
• Number of students in Science= 8x

If 150 more students join Arts faculty:

• 5x+150

80 more students join science faculty:

• 8x+80

The respective ratio becomes 3:4

So, according to the question:

$\sf\dfrac{5x+150}{8x+80}$ = $\bf\dfrac{3}{4}$

Cross multiply:

24x+240 = 20x + 600

4x+240 = 600

4x = 360

x = 90

Original number of students:

5x+8x = 13x

13 $\times$ 90

$\sf{1170}$