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Shantanu decided to collect money for …

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Shantanu decided to collect money for buying motorcycle whose cost is ₹ 200,000. The initial amount in his Bank account is ₹ 50,000. On the basis of past drives, it is determined that after t months the beginning of the drive, the rate dx/dt at which money is arranged for his motorcycle is proportional to the difference between the desired goal of ₹ 200,000 and the total amount x in the Bank account at that time. After one month, a total of ₹ 100,000 is in the Bank account. Now answer the following questions using differential equation method:
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