What sum will amount to ₹2782.50 in 2 years at compound interest, if the rates are 5% and 6% for the successive years?

If the rates are different then formula is,

$A = P\Big(1 + \dfrac{r$1}{100}\Big)\Big(1 + \dfrac{r2}{100}\Big)

Substituting values we get,

$A = P\Big(1 + \dfrac{5}{100}\Big)\Big(1 + \dfrac{6}{100}\Big) \\[1em] \Rightarrow 2782.50 = P\Big(1 + \dfrac{1}{20}\Big)\Big(1 + \dfrac{3}{50}\Big) \\[1em] \Rightarrow 2782.50 = P \times \dfrac{21}{20} \times \dfrac{53}{50} \\[1em] \Rightarrow P = \dfrac{2782.50 \times 20 \times 50}{21 \times 53} \\[1em] \Rightarrow P = ₹2500.$

Hence, sum = ₹2500.