Simple Interest - 05

Explanation:-

$$\eqalign{ & {\text{P}} = {\text{Rs}}{\text{. 21250}} \cr & {\text{S}}{\text{.I}}{\text{.}} \cr & = {\text{Rs}}{\text{. }}\left( {{\text{26350}} - {\text{21250}}} \right) \cr & = {\text{Rs}}{\text{. }}5100 \cr & {\text{T}} = {\text{6 years}}{\text{.}} \cr & \therefore {\text{Rate}} = \left( {\frac{{100 \times 5100}}{{{\text{21250}} \times {\text{6}}}}} \right)\% \cr & = 4\% \cr}$$

Explanation:-

Let the amount invested = Rs. P
According to the questions,
$$\eqalign{ & \Leftrightarrow \frac{{{\text{P}} \times 9 \times {\text{2}}}}{{100}} + \frac{{{\text{P}} \times {\text{10}} \times {\text{2}}}}{{100}} = 760 \cr & \Leftrightarrow \frac{{\left( {18{\text{P + 20P}}} \right)}}{{100}} = 760 \cr & \Leftrightarrow 38{\text{P = 76000}} \cr & \Leftrightarrow {\text{P = 2000}} \cr}$$
Alternate
Total interest percent
$$\eqalign{ & {\text{ = }}\left( {9 \times 2} \right)\% + \left( {10 \times 2} \right)\% \cr & \Rightarrow 38\% = 760 \cr & \Rightarrow 100\% = 2000 \cr}$$
Hence required principal
= Rs. 2000

Explanation:-

$$\eqalign{ & {\text{Amount Rs 7000}} \cr & {\text{Total interest in 5 years}} \cr & {\text{ = 5}} \times \frac{{10}}{3}\% = \frac{{50}}{3}\% = \frac{1}{6} \cr}$$

Principal	Amount
6	(6 + 1)
↓ × 1000	↓ × 1000
6000	7000

Hence required principal = Rs. 6000

Explanation:-

$$\eqalign{ & {\text{P}} = {\text{Rs}}{\text{. 9534}} \cr & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {{\text{11442}} - {\text{9534}}} \right) \cr & \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.1908}} \cr & {\text{R}} = {\text{4}}\% \cr & \therefore {\text{Time}} = \left( {\frac{{{\text{100}} \times {\text{1908}}}}{{{\text{9534}} \times {\text{4}}}}} \right){\text{years}} \cr & = \left( {\frac{{{\text{47700}}}}{{{\text{9534}}}}} \right){\text{years}} \approx {\text{5 years}} \cr}$$

Explanation:-

$$\eqalign{ & {\text{P}} = {\text{Rs}}{\text{.}}\,{\text{450}} \cr & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{. 81}} \cr & {\text{R}} = {\text{4}}{\text{.5}}\% \cr & {\text{Time}} \cr & = \left( {\frac{{100 \times 81}}{{450 \times 4.5}}} \right){\text{years}} \cr & = 4\,{\text{years}}{\text{.}} \cr}$$

Explanation:-

(Principal + Interest) in 5 years → 520
(Principal + Interest) in 7 years → 568
$$\eqalign{ & \therefore {\text{Interest in 2 years = 48}} \cr & \therefore {\text{I = }}\frac{{{\text{48}}}}{2}{\text{ }} \cr & \,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 24 in one year}} \cr & \therefore {\text{P = 520 - 24}} \times {\text{5}} \cr & \,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 400}} \cr}$$

Explanation:-

Let the sum at 8% be Rs. x.
Let the sum at 5% be 1550 - x.
According to the given condition,
$$\eqalign{ & \frac{{{\text{x}} \times 8 \times 3}}{{100}} + \frac{{\left( {1550 - {\text{x}}} \right) \times 5 \times 3}}{{100}} = 300 \cr & \Rightarrow \frac{{24{\text{x}} + \left( {1550 - {\text{x}}} \right) \times 15}}{{100}} = 300 \cr & \Rightarrow \frac{{24{\text{x}} + 23250 - 15{\text{x}}}}{{100}} = 300 \cr & \Rightarrow 24{\text{x}} - 15{\text{x}} = 30000 - 23250 \cr & \Rightarrow 24{\text{x}} - 15{\text{x}} = 6750 \cr & \Rightarrow 9{\text{x}} = 6750 \cr & \Rightarrow {\text{x}} = \frac{{6750}}{9} = 750 \cr & \frac{{{\text{Money lent at 5}}\% }}{{{\text{Money lent at 8}}\% }} \cr & = \frac{{1550 - 750}}{{750}} \cr & = \frac{{800}}{{750}} \cr & = \frac{{16}}{{15}} \cr}$$

Explanation:-

Let the amounts invested in schemes A and B be Rs. 5x and 4x respectively.
then,
$$\eqalign{ & {\text{5x}} = {\text{20000}} \Rightarrow {\text{x}} = {\text{4000}}{\text{.}} \cr & \therefore {\text{Amount invested in scheme B}} \cr & = {\text{Rs}}{\text{.16000}}{\text{.}} \cr & {\text{Total interest received on maturity}} \cr & = {\text{Rs}}{\text{.}}\left[ {{\text{120}}\% {\text{ of}}\left( {\frac{{{\text{20000}} \times {\text{8}} \times {\text{5}}}}{{{\text{100}}}}} \right) + \left( {\frac{{{\text{16000}} \times {\text{9}} \times {\text{5}}}}{{{\text{100}}}}} \right)} \right] \cr & = {\text{Rs}}{\text{. }}\left( {{\text{120}}\% \,{\text{of}}\,{\text{8000}} + {\text{7200}}} \right) \cr & = {\text{Rs}}{\text{. }}\left( {{\text{9600}} + {\text{7200}}} \right) \cr & = {\text{Rs}}{\text{. 16800}}{\text{.}} \cr & \therefore {\text{Total amount}} \cr & = {\text{Rs}}{\text{. }}\left( {{\text{20000}} + {\text{16000}} + {\text{16800}}} \right) \cr & = {\text{Rs}}{\text{. 52800}}{\text{.}} \cr}$$

Explanation:-

$$\eqalign{ & {\text{Gain in 2 years}} \cr & = \left[ {\left( {5000 \times \frac{{25}}{4} \times \frac{2}{{100}}} \right) - \left( {\frac{{5000 \times 4 \times 2}}{{100}}} \right)} \right] \cr & = {\text{Rs}}{\text{.}}\left( {625 - 400} \right) \cr & = {\text{Rs}}{\text{. }}225. \cr & \therefore {\text{Gain 1 year}} = {\text{Rs}}{\text{.}}\left( {\frac{{225}}{2}} \right) \cr & = {\text{Rs}}{\text{. }}112.50 \cr}$$

Explanation:-

$$\eqalign{ & {\text{Let principal = 5 units}} \cr & {\text{Hence interest}} \cr & {\text{ = 5}} \times \frac{2}{5} \cr & {\text{ = 2 units}} \cr & {\text{Time = 10 years}} \cr & {\text{By using formula, }} \cr & {\text{Rate% = }}\frac{2}{5} \times \frac{{100}}{{10}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 4% }} \cr}$$