[Rs. 20000] Mr. Mani invested an amount of Rs. 12000 at the simple interest rate of 10% per annum and another am

Mr. Mani invested an amount of Rs. 12000 at the simple interest rate of 10% per annum and another amount at the simple interest rate of 20% 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.

Rs. 25000

Rs. 15000

Rs. 10000

Rs. 20000

Explanation:

-------------------------------------------------------------------------------------

Solution 1

-------------------------------------------------------------------------------------

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

-------------------------------------------------------------------------------------

Solution 2

-------------------------------------------------------------------------------------

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

Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?	Answer
Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?	Answer
An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:	Answer
A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:	Answer
A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?	Answer
A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:	Answer
A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6$ \dfrac{1}{4} $ p.a for 2 years. Find his gain in the transaction per year.	Answer
If simple interest on a certain sum of money for 8 years at 4% per annum is same as the simple interest on Rs. 560 for 8 years at the rate of 12% per annum then the sum of money is	Answer
A lent Rs. 4000 to B for 2 years and Rs. 2000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is :	Answer
Mr. Mani invested an amount of Rs. 12000 at the simple interest rate of 10% per annum and another amount at the simple interest rate of 20% 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