The decline of traditional exports of cotton and silk manufacturers in the face of Manchester competition did not raise acute remittance problems for the East India Company, servants of the company, and private traders. Let's discuss each of these options in detail:

a) East India Company:
The East India Company was a British trading company that had a monopoly on trade between Britain and the Indian subcontinent. It had established its own factories and trading posts in India, which primarily dealt with the export of raw materials like cotton and silk. However, with the rise of Manchester's industrial production, the demand for Indian cotton and silk declined.

The East India Company was not significantly affected by this decline in traditional exports. This is because the company had diversified its trade and invested in other profitable commodities such as tea, opium, and indigo. These new revenue streams helped offset the losses from the declining cotton and silk exports. Additionally, the company had a strong financial base and access to capital, which allowed it to weather the impact of Manchester competition without facing acute remittance problems.

b) Servants of the Company:
The servants of the East India Company, including administrators, officials, and military personnel, were not directly involved in the export of cotton and silk. Their salaries and remittances were primarily paid by the company itself, rather than being dependent on the revenue generated from these exports. Therefore, the decline in traditional exports did not raise acute remittance problems for the servants of the company.

c) Private traders:
Private traders, who were engaged in the export of cotton and silk, may have faced challenges due to the competition from Manchester. However, it is mentioned in the question that the decline in traditional exports did not raise acute remittance problems for private traders. This implies that while they might have experienced some decline in profits, it did not lead to severe financial difficulties or remittance problems.

In conclusion, the decline of traditional exports of cotton and silk manufacturers in the face of Manchester competition did not raise acute remittance problems for the East India Company, servants of the company, and private traders. These entities either had alternative revenue streams, a stable source of income, or were able to manage the impact of competition without facing severe financial difficulties. Therefore, the correct answer is option 'D' - None of these.