Question

The value of an estate in January 1905 started gradually declining in such a way that at the end of each year it was worth only x times its value at the beginning of the year. What was its worth in end December 1910 ?
(1) It was worth Rs. 10109 in the end of December 1906
(2) It was worth Rs. 12345 in the beginning of January 1905.

Answer 1

Let rate of declining per annum be $y$.

Now,

According to given information, from January $1905$ to December $1905$, time $=2$ years

Therefore, $12345-\frac{12345\times y\times 2}{100}=10109$

By solving we get $y=9.05\%$

Now,

Value in December $1905=12345-\frac{12345\times 9.05\times 6}{100}=$ Rs. $5641.665$