Explanation:

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Solution 1

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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

$\text{Simple Interest = }\dfrac{\text{PRT}}{100} = \dfrac{12000 \times 10 \times 1}{100} = \text{Rs. 1200}$

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

$\text{Simple Interest = }\dfrac{\text{PRT}}{100} = \dfrac{x \times 20 \times 1}{100} = \text{Rs.}\dfrac{x}{5}$

$\text{Total interest = Rs.}\left(1200 + \dfrac{x}{5}\right)$

$\text{i.e., Rs.}\left(1200 + \dfrac{x}{5}\right)\text{ is the simple interest for Rs.(12000 + x) at 14% per annum for 1 year}$

$\Rightarrow \left(1200 + \dfrac{x}{5}\right) = \dfrac{(12000 + x) \times 14 \times 1}{100}$

$\Rightarrow 120000 + 20x = 14 \times 12000 + 14x$

$\Rightarrow 6x = 14 \times 12000 - 120000 = 48000$

$\Rightarrow x = 8000$

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

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Solution 2

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If an amount P₁ is lent out at simple interest of R₁% per annum and another amount P₂ at simple interest

rate of R₂% per annum, then the rate of interest for the whole sum can be given by

$\text{R} = \dfrac{\text{P}_1\text{R}_1 + \text{P}_2\text{R}_2}{\text{P}_1+\text{P}_2}$

P₁ = Rs. 12000, R₁ = 10%

P₂ = ?, R₂ = 20%

R = 14%

$14 = \dfrac{12000 \times 10 + \text{P}_2 \times 20}{12000 +\text{P}_2}$

12000 $\times 14 + 14\text{P}_2$ = 120000 + 20$\text{P}_2$

6$\text{P}_2$ = 14$ \times 12000$ - 120000 = 48000

$\Rightarrow \text{P}_2 = 8000$

Total amount invested = (P₁ + P₂) = $\left(12000 + 8000\right)$ = Rs. 20000