A sum of money becomes ₹35,680 after 3 years and ₹53,520 after 6 years at a certain rate percentage p.a., interest compounded yearly. What is the compound interest on the same sum in the first case? (Your answer should be nearest to an integer)

We know that the formula A = $$ p (1+ \dfrac{R}{100})^t $$

then put the value from the given question $$ 35680 = p (1 + \dfrac{R}{100} )^3 $$  ........ equestion (1) 

  and again put the value $$ 53520 = p (1+ \dfrac{R}{100})^6 $$   .............. equeston (2)

so divide equestion(1) from equestoin (2) 

$$\Rightarrow 1.5 = (1 + \dfrac{R}{100})^3 $$

$$\Rightarrow R = [(1.5)^\dfrac{1}{3} -1] \times 100 $$

put the value in equestion (1) so $$ 35680 = p \times 1.5 $$ 

$$\Rightarrow p = \dfrac{356800}{15}$$

 so compound intrest = $$ 35680 - \dfrac{356800}{15}$$

$$\Rightarrow  CI = 35680 - 23786.66 $$

$$\Rightarrow CI = 11893.34$$

$$\Rightarrow compound intrest (CI) = Rs  11,893 Ans