The students in three classes are in the ratio 2 : 3 : 5. If 40 studen

1.	The students in three classes are in the ratio 2 : 3 : 5. If 40 students are increased in each class, the ratio changes to 4 : 5 : 7. Originally the total number of students was (a) 100 (b) 180 (c) 200 (d) 400
Answer» (c) 200 In the beginning, the three classes had 2x, 3x and 5x students where x is a constant of proportionality. 40 students were added in each section. ⇒ There are 2k + 40, 3k + 40 and 5k + 40 number of students in each section. Given, 2k + 40 : 3k + 40 : 5k + 40 = 4 : 5 : 7 ⇒ \(\frac{2k+40}{3k+40}=\frac45\) ⇒ 10k + 200 = 12k + 160 ⇒ 2k = 40 ⇒ k = 20 ∴ Originally the total number of students was 2 × 20 + 3 × 20 + 5 × 20 = 200.

The students in three classes are in the ratio 2 : 3 : 5. If 40 students are increased in each class, the ratio changes to 4 : 5 : 7. Originally the total number of students was (a) 100 (b) 180 (c) 200 (d) 400

Answer»

(c) 200

In the beginning, the three classes had 2x, 3x and 5x students where x is a constant of proportionality. 40 students were added in each section.

⇒ There are 2k + 40, 3k + 40 and 5k + 40 number of students in each section.

Given, 2k + 40 : 3k + 40 : 5k + 40 = 4 : 5 : 7

⇒ \(\frac{2k+40}{3k+40}=\frac45\) ⇒ 10k + 200 = 12k + 160

⇒ 2k = 40 ⇒ k = 20

∴ Originally the total number of students was 2 × 20 + 3 × 20 + 5 × 20 = 200.