# 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 ?

A. 2 years B. 4 years C. 5 years D. 3 years Answer: Option A
$\begin{array}{l} \mathrm{P}+\mathrm{SI}=\frac{\mathrm{P} \times \mathrm{R} \times \mathrm{T}}{100}+\mathrm{P} \\ \Rightarrow 2200=\frac{\mathrm{P} \times 5 \times \mathrm{T}}{100}+\mathrm{P} \\ \Rightarrow 2200 \times 100=5 \mathrm{PT}+100 \mathrm{P} \ldots \ldots \ldots \text { (i) } \\ \Rightarrow 2320=\frac{\mathrm{P} \times 8 \times \mathrm{T}}{100}+\mathrm{P} \\ \Rightarrow 2320 \times 100=8 \mathrm{PT}+100 \mathrm{P} \\ \Rightarrow 2320 \times 100=3 \mathrm{PT}+5 \mathrm{PT}+100 \mathrm{P} \ldots \end{array}$ 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 $\begin{array}{l} \Rightarrow \mathrm{P}=\frac{200000}{100} \\ \Rightarrow \mathrm{P}=\text { Rs } 2000 \end{array}$ Using This Formula, $\begin{array}{l} \left(\because \mathrm{SI}=\frac{\mathrm{P} \times \mathrm{R} \times \mathrm{T}}{100}\right) \\ \therefore 200=\frac{2000 \times 5 \times \mathrm{T}}{100} \\ \Rightarrow \mathrm{T}=\frac{200}{100}=2 \text { years } \end{array}$
Alternate Solution $\begin{array}{l} (8-5) \%=2320-2200 \\ \Rightarrow 3 \%=120 \\ \Rightarrow 1 \%=40 \\ \Rightarrow 5 \%=200 \\ \text { Principal }=2200-200 \\ =\text { Rs. } 2000 \\ \text { SI }=\frac{\mathrm{P} \times \mathrm{R} \times \mathrm{T}}{100} \\ \Rightarrow 200=\frac{2000 \times 5 \times \mathrm{T}}{100} \\ \Rightarrow \mathrm{T}=\frac{200}{100}=2 \text { years } \end{array}$