When simple interest is charged a certain principle amounts to Rs. 7400 in 4 years and Rs. 9200 in 7 years.

Correct option is (D) 12%

Let principal amount be Rs x and rate of interest be R%.

Given that total amount after applying simple interest on principal amount in 4 years is Rs 7400 & in 7 years Rs 9200.

\(\therefore\) \(x+\frac{4xR}{100}=7400\)       __________(1)

and \(x+\frac{7xR}{100}=9200\)   __________(2)

From (1), we obtain

xR = 25 (7400 - x)

\(\Rightarrow\) xR = 185000 - 25x   __________(3)

Then from (2) & (3), we get

\(x+\frac{7(185000 - 25x)}{100}=9200\)

\(\Rightarrow\) 4x + 51800 - 7x = 36800    (Multiplying both sides by 4)

\(\Rightarrow\) -3x = 36800 - 51800

\(\Rightarrow\) -3x = -15000

\(\Rightarrow x=\frac{-15000}{-3}=5000\)

Then from (3), we get

5000R = 185000 - 125000

\(\Rightarrow\) 5000R = 60000

\(\Rightarrow R=\frac{60000}{5000}=\frac{60}{5}=12\)

Hence, rate of interest is 12%.

Correct option is D) 12%