Was the Muslim population of India in 1850, 16% of the total population?

Question

According to http://www.kashmirherald.com/featuredarticle/indiacensus.html

To put it in broader perspective, Muslim population has steadily grown from 13% in 1800 to 16% in 1850 to 20% in 1900 to 25% in 1947 and anywhere between 30 to 33% today taking into account the geographical area of pre-partitioned India. These statistics are available from various sources.

Google gave me this which has the exact claim but doesn't cite any source:

5. In broad terms, the Muslim population in India has been growing in geometrical progression vis-à-vis Hindus who have been growing in arithmetical progression. And with the improvement of educational and economic level of the Hindus, the disparity has become even more pronounced. To put it in broader perspective, Muslim population has steadily grown from 13% in 1800 to 16% in 1850 to 20% in 1900 to 25% in 1947 and anywhere between 30 to 33% today taking into account the geographical area of pre-partitioned India. These statistics are available from various sources.

Was the Muslim population of India in 1850, 16% of the total population?

Answer 1

The ~1855 book The British Colonies: Their History, Extent, Condition and Resources, Volume 11 has a section titled "PROPORTION OF MOSLEMS TO HINDOOS".

Clearly, there was no complete census. However there is a statement that the previous estimate of the "total Mohammedan population in India" of 15 million Muslims is justified by recent investigations. The book gives estimates of the total population such as 172 Million.

For quantitative data the book reports a 1851 Madras region census which finds:

1,679,847 "Mohammedans and others" and 19,901,725 "Hindoos".

That's about 8% Muslim and other.

A 1852 census of "The N.W. Provinces" found:

4,547,771 "Mohammedans and others" and 25,724,109 "Hindoos"

That's about 15% Muslim and other.

(see the appendix at pages 552-554 for further details.)

The 1856 book India, Ancient and Modern at page 488 says:

The Mohammedans of India are variously estimated at 1/8, 1/10, 1/12 of the entire population of the country.

This book also says about 15 to 18 million Muslims out of a total population of 150 million.

So overall, the proportion of Muslims wasn't precisely known, but the 16% value in the OP is above the range of estimates made at the time (1850), which was 8-13%.