Solution:
$$\eqalign{ \frac{{{\text{Principal}}}}{{{\text{Amount}}}} = \frac{{4 \times 5}}{{5 \times 5}} \cr \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{20}}{{25}} \cr {\text{After three year}} \cr \frac{{\text{P}}}{{\text{A}}} = \frac{{5 \times 4}}{{7 \times 4}} \cr \,\,\,\,\,\,\,\, = \frac{{20}}{{28}} \cr {\text{In three year S}}{\text{.I}}{\text{.}} \cr = 28x - 25x \cr = 3x \cr \text{So, the required interest will be} \cr 3x = \frac{{20x \times {\text{R}} \times 3}}{{100}} \cr {\text{R}} = 5\% \cr} $$

Solution:
$$\eqalign{ {\text{Sum of the 12 years age }} \cr {\text{ = Rs}}{\text{. 100000}} \cr {\text{Sum of the 18 years age }} \cr = {\text{P}} + \frac{{{\text{P}} \times {\text{R}} \times {\text{T}}}}{{100}} \cr = {\text{100000}} + \frac{{100000 \times 6 \times 6}}{{100}} \cr = {\text{100000}} + {\text{36000}} \cr = {\text{136000}} \cr} $$
Total expenses
= 2500 + 500 = 3000 per year
Total expenses ( 6 years )
= 3000 × 6 = Rs. 18000
Amount obtained
= 136000 - 18000
= 118000

Solution:
$$\eqalign{ {\text{Let the sum be Rs}}{\text{. }}x{\text{ and}} \cr {\text{original rate be R}}\% \cr {\text{Then,}} \cr \Rightarrow \frac{{x \times \left( {{\text{R}} + 1} \right) \times 3}}{{100}} - \frac{{x \times {\text{R}} \times 3}}{{100}} = 5100 \cr \Rightarrow 3{\text{R}}x + 3x - 3{\text{R}}x = 510000 \cr \Rightarrow 3x = 510000 \cr \Rightarrow x = 170000. \cr {\text{Hence,}} \cr {\text{Sum}} = {\text{Rs}}.170000 \cr} $$

Solution:
$$\eqalign{ 9/8 \cr {\text{Principle}} = 8{\text{ unit}} \cr {\text{Amount}} = 9{\text{ unit}} \cr {\text{Interest}} = 9.8{\text{ unit}} \cr {\text{S}}{\text{.I}}{\text{.}} = \frac{{8 \times 5 \times R}}{{100}} \cr 1 = \frac{{40 \times R}}{{100}} \cr R = \frac{{10}}{4} = 2.5\% {\text{ p}}{\text{.a}}{\text{.}} \cr} $$

Solution:
10% of Rs. 3 Lacs = 30000
6% of Rs. 3 Lacs = 18000
1 month interest income = 2000
∴ 1 year interest income = 2000 × 12 = 24000
Profit of Bank = 24000 - 18000 = 6000
Profit of Post Office = 30000 - 24000 = 6000
∴ Ratio of profit = 6000 : 6000 = 1 : 1
So, amount deposited = Rs. 150000 each
And difference = 0

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

Solution:
$$\eqalign{ {\text{Let}}\,{\text{rate}}\,{\text{is}}\,R\% \cr {\text{According}}\,{\text{to}}\,{\text{the}}\,{\text{question}}, \cr \left[ {\frac{{400 \times 2 \times R}}{{100}}} \right] + \left[ {\frac{{100 \times 4 \times R}}{{100}}} \right] = 60 \cr 8R + 4R = 60 \cr {\text{Hence}},\,R = 5\% \cr} $$