Question

Mani invested an amount of rs. 12000 at a rate of 10% simple interest per annum and another amount at a rate of 20% simple interest per annum. the total interest earned at the end of one year on the total amount invested became 14% per annum. find the total amount invested.

Answer 1

Hey there,

Answer:
Rs. 20,000
Explanation:
Let his investments be Rs.12000 and Rs.x

Rs. 12000 is invested at the simple interest rate of 10% per annum for 1 year

Simple Interest = PRT100=12000×10×1100=Rs. 1200

Rs. x is invested at the simple interest rate of 20% per annum for 1 year

Simple Interest = PRT100=x×20×1100=Rs.x5

Total interest = Rs.(1200+x5)i.e., Rs.(1200+x5) is the simple interest for Rs.(12000 + x) at 14% per annum for 1 year⇒(1200+x5)=(12000+x)×14×1100⇒120000+20x=14×12000+14x⇒6x=14×12000−120000=48000⇒x=8000

Total amount invested = 12000 + x = 12000 + 8000 = Rs. 20000

Hope this helps!

Answer 2

Let his investments be Rs.12000 and Rs.xRs. 12000 is invested at the simple interest rate of 10% per annum for 1 year$MF#%\text{Simple Interest =}\dfrac{\text{PRT}}{100} = \dfrac{12000\times 10 \times 1}{100} = \text{Rs. 1200}$MF#%Rs. x is invested at the simple interest rate of 20% per annum for 1 year$MF#%\text{Simple Interest =}\dfrac{\text{PRT}}{100} = \dfrac{x \times20 \times 1}{100} = \text{Rs.}\dfrac{x}{5}$MF#%$MF#%\begin{align}&\text{Total interest= Rs.}\left(1200 + \dfrac{x}{5}\right)\\\\&\text{i.e., Rs.}\left(1200 + \dfrac{x}{5}\right)\text{ is the simple interest for Rs.(12000 + x) at 14% per annum for 1 year}\\\\ &\Rightarrow \left(1200 +\dfrac{x}{5}\right) = \dfrac{(12000 + x)\times 14 \times 1}{100}\\\\ &\Rightarrow 120000 + 20x = 14 \times 12000 + 14x\\\\&\Rightarrow 6x = 14 \times 12000 - 120000= 48000\\\\ &\Rightarrow x = 8000\end{align}$MF#%Total amount invested = 12000 + x = 12000 + 8000 = Rs. 20000