A certain sum of money amounts to Rs 1284 in 7 years and Rs 2568 in 19 years by Simple Interest rate. If the rate of interest is doubled, then what is the compound interest for 2 years with the same principal?

Let P be principal and R be rate. Amount after 7 years: P + 7PR = 1284. Amount after 19 years: P + 19PR = 2568. Subtracting gives 12PR = 1284, so PR = 107. Then P = 1284 - 7(107) = 535, R = 107/535 = 20%. When rate doubles to 40%, CI for 2 years = P[(1 + 0.4)^2 - 1] = 535[1.96 - 1] = 535(0.96) = 513.6. This matches option B.