British Education Policy in India had a significant impact on the development of education in the country. The two statements mentioned in the question are related to key policies implemented by the British government during their colonial rule in India. Let's analyze each statement individually:

1. Woods dispatch (1854) brought downward filtration theory:
- The Woods Dispatch of 1854 was a landmark policy document that laid down the principles for the development of education in India under British rule.
- The dispatch was named after Sir Charles Wood, the President of the Board of Control for India at that time.
- The Woods Dispatch emphasized the need for a systematic and well-regulated education system in India.
- It aimed to promote education among the masses and create a class of Indians who would be educated enough to assist the British administration.
- The dispatch introduced the concept of "downward filtration theory," which meant that education should start at the top and gradually filter down to the lower levels of society.
- According to this theory, the British government focused on providing education to the upper classes, such as the elite Indians and the British officials' children, with the hope that the benefits of education would eventually trickle down to the lower classes.
- However, this policy resulted in limited access to education for the majority of the Indian population, as it mainly catered to the needs of the privileged few.

2. Charter Act of 1813 sanctioned 1 lakh rupees for educational development:
- The Charter Act of 1813 was an important legislation passed by the British Parliament regarding the governance of British India.
- The act had provisions related to various aspects of British rule in India, including trade, administration, and education.
- One of the significant provisions of the Charter Act of 1813 was the allocation of 1 lakh rupees annually for the promotion of education in India.
- This marked the first official recognition and financial support from the British government for educational development in the country.
- The fund was primarily used for the establishment of schools and colleges, especially in urban areas.
- However, it is important to note that the educational institutions established with this fund were primarily focused on providing Western-style education and promoting British culture and values.

In conclusion, both statements are correct. The Woods Dispatch of 1854 introduced the concept of downward filtration theory, emphasizing education for the upper classes, while the Charter Act of 1813 sanctioned 1 lakh rupees annually for educational development in India. These policies had a significant impact on the education system during British colonial rule in India.