A certain sum of money amount to Rs 2200 at 5% interest Rs 2320 at 8% interest in the same period of time. The period of time is = ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{P}} + {\text{SI = }}\frac{{{\text{P}} \times {\text{R}} \times {\text{T}}}}{{100}} + {\text{P}} \cr & \Rightarrow 2200{\text{ = }}\frac{{{\text{P}} \times 5 \times {\text{T}}}}{{100}} + {\text{P}} \cr} $$
⇒ 2200 × 100 = 5PT + 100P ......... (i)
$$ \Rightarrow 2320 = \frac{{{\text{P}} \times 8 \times {\text{T}}}}{{100}} + {\text{P}}$$
⇒ 2320 × 100 = 8PT + 100P
⇒ 2320 × 100 = 3PT + 5PT + 100P ............(ii)
Value of equation (i) put equation (ii)
⇒ 2320 × 100 = 3PT + 2200 × 100
⇒ 3PT = 120 × 100
⇒ PT = 4000
Value of PT in equation (i)
⇒ 2200 × 100 = 5 × 4000 + 100P
⇒ 220000 - 20000 = 100P
$$\eqalign{ & \Rightarrow {\text{P = }}\frac{{200000}}{{100}} \cr & \Rightarrow {\text{P = Rs 2000}} \cr & {\text{Using this formula}} \cr & \left( {\because {\text{SI = }}\frac{{{\text{P}} \times {\text{R}} \times {\text{T}}}}{{100}}} \right) \cr & \therefore {\text{200}} = \frac{{2000 \times 5 \times {\text{T}}}}{{100}} \cr & \Rightarrow {\text{T}} = \frac{{200}}{{100}}{\text{ = 2 years}} \cr & \cr & {\text{ }}{\bf{Alternate:}} \cr & \left( {8 - 5} \right)\% = 2320 - 2200 \cr & \Rightarrow 3\% = 120 \cr & \Rightarrow 1\% = 40 \cr & \Rightarrow 5\% = 200 \cr & {\text{Principal = 2200 - 200}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 2000}} \cr & {\text{SI = }}\frac{{{\text{P}} \times {\text{R}} \times {\text{T}}}}{{100}} \cr & \Rightarrow {\text{200}} = \frac{{2000 \times 5 \times {\text{T}}}}{{100}} \cr & \Rightarrow {\text{T}} = \frac{{200}}{{100}}{\text{ = 2 years}} \cr} $$