Aptitude Simple Interest Practice QA

Let the sum invested in Scheme A be Rs. $ x $ and that in Scheme B be Rs.13900 - x.

Then,$ \left(\dfrac{x \times 14 \times 2}{100} \right) $+$ \left(\dfrac{(13900 - x) \times 11 \times 2}{100} \right) $= 3508

$\Rightarrow$ 28$ x $ - 22$ x $ = 350800 - $\left(13900 \times 22\right)$

$\Rightarrow$ 6$ x $ = 45000

$\Rightarrow x $ = 7500.

So, sum invested in Scheme B = Rs. $\left(13900 - 7500\right)$ = Rs. 6400.

Let rate = R% and time = R years.

Then,$ \left(\dfrac{1200 \times R \times R}{100} \right) $= 432

$\Rightarrow$ 12R² = 432

$\Rightarrow$ R² = 36

$\Rightarrow$ R = 6.

Let the sum be Rs. 100. Then,

S.I. for first 6 months = Rs.$ \left(\dfrac{100 \times 10 \times 1}{100 \times 2} \right) $= Rs. 5

S.I. for last 6 months = Rs.$ \left(\dfrac{105 \times 10 \times 1}{100 \times 2} \right) $= Rs. 5.25

So, amount at the end of 1 year = Rs. $\left(100 + 5 + 5.25\right)$ = Rs. 110.25

$\therefore$ Effective rate = $\left(110.25 - 100\right)$ = 10.25%

Let the rate be R% p.a.

Then,$ \left(\dfrac{5000 \times R \times 2}{100} \right) $+$ \left(\dfrac{3000 \times R \times 4}{100} \right) $= 2200.

$\Rightarrow$ 100R + 120R = 2200

$\Rightarrow$ R =$ \left(\dfrac{2200}{220} \right) $= 10.

$\therefore$ Rate = 10%.

Let the original rate be R%. Then, new rate = (2R)%.

Note:

Here, original rate is for 1 year(s); the new rate is for only 4 months i.e. $\dfrac{1}{3}$ year(s).

$\therefore \left(\dfrac{725 \times R \times 1}{100} \right) $+$ \left(\dfrac{362.50 \times 2R \times 1}{100 x 3} \right) $= 33.50

$\Rightarrow$ $\left(2175 + 725\right)$ R = 33.50 x 100 x 3

$\Rightarrow$ $\left(2175 + 725\right)$ R = 10050

$\Rightarrow$ $\left(2900\right)$R = 10050

$\Rightarrow$ R =$ \dfrac{10050}{2900} $= 3.46

$\therefore$ Original rate = 3.46%

S.I. for 3 years = Rs. $\left(12005 - 9800\right)$ = Rs. 2205.

S.I. for 5 years = Rs.$ \left(\dfrac{2205}{3} \times 5\right) $= Rs. 3675

$\therefore$ Principal = Rs. $\left(9800 - 3675\right)$ = Rs. 6125.

Hence, rate =$ \left(\dfrac{100 \times 3675}{6125 \times 5} \right) $%= 12%

Gain in 2 years = Rs.$ \left(\left(5000 \times\dfrac{25}{4} \times\dfrac{2}{100} \right)-\left(\dfrac{5000 \times 4 \times 2}{100} \right)\right) $

= Rs. $\left(625 - 400\right)$

= Rs. 225.

$\therefore$ Gain in 1 year = Rs.$ \left(\dfrac{225}{2} \right) $= Rs. 112.50

Let the sum of money be x

then

$\dfrac{x \times 4 \times 8}{100 } = \dfrac{560 \times 12 \times 8}{100 }$

$x \times 4 \times 8 = 560 \times 12 \times 8$

$x \times 4 = 560 \times 12$

$x = 560 \times 3 = 1680$

Let the rate of interest per annum be R%

Simple Interest for Rs.4000 for 2 years at R% + Simple Interest for Rs.2000 for 4 years at R%

= 2200

$\dfrac{4000 \times \text{R} \times 2}{100} + \dfrac{2000 \times \text{R} \times 4}{100} = 2200$

80$\text{R} + 80 \text{R} $= 2200

160$\text{R} = 2200$

16$\text{R} = 220$

4$\text{R} = 55$

$\text{R} = \dfrac{55}{4} = 13.75\%$

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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

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