Simple Interest - 01

Explanation:-

Let Ram get Rs. x and
Shyam get Rs. (260200 - x)
Then Amount get by Ram after 3 years
$${\text{ = }}x \times {\left( {1 + \frac{4}{{100}}} \right)^3}$$
and Amount get by Shyam after 6 years
$$= \left( {260200 - x} \right) \times {\left( {1 + \frac{4}{{100}}} \right)^6}$$
$$\eqalign{ & {\text{But both get equal amount }} \cr & \therefore x \times {\left( {1 + \frac{4}{{100}}} \right)^3} = \left( {260200 - x} \right) \times {\left( {1 + \frac{4}{{100}}} \right)^6} \cr & \Rightarrow \frac{x}{{2600200 - x}} = \frac{{17576}}{{15625}} \cr & \Rightarrow 15625x = 4573275200 - 17576x \cr & \Rightarrow 33201x = 4573275200 \cr & \Rightarrow x = 137745.022 \cr}$$

Explanation:-

S.I for 1 year = 5832 – 5182 = Rs. 650
S.I for 2 years = Rs. 1300
P = 5182 – 1300
= Rs. 3882

Explanation:-

Let the amount invested in scheme A be Rs. x and that in B be Rs. 3x.
Then,
$$\eqalign{ & = \frac{{x \times 4 \times 8}}{{100}} + \frac{{3x \times 2 \times 13}}{{100}} = 1320 \cr & or,\,\frac{{32x}}{{100}} + \frac{{78x}}{{100}} = 1320 \cr & or,\,\frac{{110x}}{{110}} = 1320 \cr & \therefore x = \frac{{1320 \times 100}}{{110}} \cr & = {\text{Rs}}{\text{. 1200}}. \cr}$$

Explanation:-

$$\eqalign{ & {\text{Rate}} = \frac{{{\text{S}}{\text{.I}}{\text{.}} \times {\text{100}}}}{{{\text{Principal}} \times {\text{Time}}}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{5400 \times 100}}{{15000 \times 3}} \cr & = 12\% \,{\text{Per annum}}{\text{.}} \cr}$$

Explanation:-

$$\eqalign{ & {\text{Let S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{. }}x \cr & {\text{Time}} = 10\,{\text{years}} \cr & \therefore {\text{Rate}} = \frac{{{\text{S}}{\text{.I}}{\text{.}} \times {\text{100}}}}{{{\text{Principal}} \times {\text{Time}}}} \cr & = \frac{{x \times 100}}{{x \times 10}} \cr & = 10\% \,{\text{per}}\,{\text{annum}}{\text{.}} \cr}$$

Explanation:-

$$\eqalign{ & {\text{Let principal and SI is}} \cr & {\text{ = }}10x,{\text{ }}3x{\text{ }} \cr & {\text{and time is = }}t \cr & \Rightarrow 3x = \frac{{10x \times 6 \times t}}{{100}} \cr & \Rightarrow t = 5\,{\text{years}} \cr}$$

Explanation:-

Money is double itself means interest is equal to money.
$$\eqalign{ & {\text{P = }}\frac{{{\text{P}} \times {\text{8}} \times {\text{r}}}}{{100}} \cr & \Rightarrow {\text{r = }}\frac{{100}}{8} \cr & \Rightarrow {\text{r = 12}}\frac{1}{2}\% \cr}$$

Explanation:-

$$\eqalign{ & {\bf{Case - I:}} \cr & {\text{SI}}\% = {\text{R}}\% \times {\text{t}} \cr & {\text{SI}}\% = {\text{5}}\% \times {\text{8}} \cr & = {\text{40}}\% \cr & {\bf{Case - II:}} \cr & {\text{SI}}\% = {\text{5}} \times {\text{r}}\% {\text{ }} \cr & {\text{According to the question}} \cr & \Rightarrow {\text{40}}\% = {\text{5}} \times {\text{r}}\% \cr & \Rightarrow {\text{r}}\% = {\text{8}}\% \cr}$$

Explanation:-

$$\eqalign{ & {\text{Rate of interest}} = {\text{5}}\% {\text{ p}}{\text{.a}}{\text{.}} \cr & {\text{sum}} = {\text{Rs}}{\text{. 3200}} \cr & {\text{Time}} = {\text{2 years 6 months}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 2\frac{1}{2}{\text{years}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{5}{2}{\text{years}} \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{{{\text{Prinicipal}} \times {\text{Time}} \times {\text{Rate}}}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\, = \frac{{3200 \times 5 \times 5}}{{2 \times 100}} \cr & \,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}400 \cr & \therefore {\text{Amount}} = {\text{Rs}}{\text{. sum}} + {\text{S}}{\text{.I}}. \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {3200 + 400} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 3600}}{\text{.}} \cr}$$

Explanation:-

Let the three amounts be Rs. x, Rs. y and Rs. z,
Then,
$$\eqalign{ & = \frac{{x \times 10 \times 6}}{{100}} = \frac{{y \times 12 \times 10}}{{100}} = \frac{{z \times 15 \times 12}}{{100}} \cr & \Rightarrow 60x = 120y = 180z \cr & \Rightarrow x = 2y = 3z = k(say) \cr & \Rightarrow x = k,y = \frac{k}{2},z = \frac{k}{3} \cr & \Rightarrow x:y:z = k:\frac{k}{2}:\frac{k}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1:\frac{1}{2}:\frac{1}{3} \cr & = 6:3:2 \cr}$$