10% of the inhabitants of a village having died of cholera, panic set in, due to which 25% of the remaining inhabitants left the village. The population of inhabitants is then reduced to 4050. Find the number of original inhabitants.a.8000b.6000c.4000d.2000
Question
10% of the inhabitants of a village having died of cholera, panic set in, due to which 25% of the remaining inhabitants left the village. The population of inhabitants is then reduced to 4050. Find the number of original inhabitants.a.8000b.6000c.4000d.2000
Solution
Let's solve this step by step:
Step 1: Let's assume the original number of inhabitants in the village was X.
Step 2: According to the problem, 10% of the inhabitants died due to cholera. So, the number of inhabitants left is 90% of X, which is 0.9X.
Step 3: Then, 25% of the remaining inhabitants left the village due to panic. So, the number of inhabitants left now is 75% of the remaining inhabitants, which is 0.75 * 0.9X = 0.675X.
Step 4: According to the problem, the number of inhabitants left now is 4050. So, we can set up the equation 0.675X = 4050.
Step 5: Solving this equation for X gives us X = 4050 / 0.675 = 6000.
So, the original number of inhabitants in the village was 6000. Therefore, the correct answer is (b) 6000.
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