Question : Before the battle, the ratio of tanks to planes in an army was 5 : 3. During the war, 1000 tanks were destroyed and 800 planes were destroyed. The ratio of tanks to planes became 2 : 1, what was the number of tanks after the war?
Option 1: 2000
Option 2: 1000
Option 3: 3000
Option 4: 4000
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Correct Answer: 2000
Solution :
Given:
Before the battle, the ratio of tanks to planes in an army was 5 : 3.
Let the number of tanks before battle = $5x$ and the number of planes before battle = $3x$.
During the war, 1000 tanks and 800 planes were destroyed.
So, the ratio becomes 2 : 1.
According to the question,
$\frac{(5x-1000)} {(3x-800)}=\frac{2}{1}$
⇒ $5x-1000 = 6x-1600$
$\therefore x = 600$
So, number of tanks after war = (600 × 5) – 1000 = 2000
Hence, the correct answer is 2000.
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