A certain sum of money amount to Rs. 2200 at 5 % p.a. Rate of interest, Rs. 2320 at 8% interest in the same period of time. The period of time is:

Let principal sum = Rs. $$100x$$ and time period = $$t$$ years

Amount under simple interest = $$P+(\frac{P\times R\times T}{100})$$

According to ques,

=> $$100x+(\frac{100x\times 5\times t}{100})=2200$$

=> $$100x+5tx=2200$$

=> $$x(20+t)=440$$

=> $$x=\frac{440}{(20+t)}$$ -------------(i)

Similarly, $$100x+(\frac{100x\times 8\times t}{100})=2320$$

=> $$100x+8tx=2320$$

=> $$x(100+8t)=2320$$

=> $$x=\frac{2320}{(100+8t)}$$ -------------(ii)

Comparing equations (i) and (ii), we get :

=> $$\frac{440}{20+t}=\frac{2320}{100+8t}$$

=> $$4400+352t=4640+232t$$

=> $$352t-232t=4640-4400$$

=> $$120t=240$$

=> $$t=\frac{240}{120}=2$$ years

=> Ans - (D)