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Before a battle, the ratio of captains to soldiers was 2 : 7. During the war 25 captains and 100 soldiers were martyred. The new ratio of captains to soldiers became 3 : 10. What is the number of soldiers after the war?

Before a battle, the ratio of captains to soldiers was 2 : 7. During the war 25 captains and 100 soldiers were martyred. The new ratio of captains to soldiers became 3 : 10. What is the number of soldiers after the war? Correct Answer 250

Let the remaining number of soldiers and captains be x and y respectively

⇒ y/x = 3/10

⇒ y = 0.3x

⇒ Original number of soldiers = x + 100

⇒ Original number of captains = y + 25 = 0.3x + 25

ATQ,

⇒ (0.3x + 25)/(x + 100) = 2/7

⇒ 2.1x + 175 = 2x + 200

⇒ 0.1x = 25

⇒ x = 250

∴ The number of soldiers after war is 250

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