Answer: Option B. -> Rs. 46305
Let the value of each instalment be Rs. x
Then, (P.W. of Rs. x due 1 year hence) + (P.W. of Rs. x due 2 year hence) + (P.W. of Rs. x due 3 year hence) = 126100
$$\eqalign{
& \Rightarrow \frac{x}{{\left( {1 + \frac{5}{{100}}} \right)}} + \frac{x}{{{{\left( {1 + \frac{5}{{100}}} \right)}^2}}} + \frac{x}{{{{\left( {1 + \frac{5}{{100}}} \right)}^3}}} = 126100 \cr
& \Rightarrow \frac{{20x}}{{21}} + \frac{{400x}}{{441}} + \frac{{8000x}}{{9261}} = 126100 \cr
& \Rightarrow \frac{{8820x + 8400x + 8000x}}{{9261}} = 126100 \cr
& \Rightarrow \frac{{25220x}}{{9261}} = 126100 \cr
& \Rightarrow x = \left( {\frac{{126100 \times 9261}}{{25220}}} \right) \cr
& \Rightarrow x = 46305 \cr} $$

Answer: Option A. -> Rs. 400
$$\eqalign{
& {\text{Rate of interest 5}}\% \cr
& = \frac{1}{{20}} \cr
& {\text{Let principal}} \cr
& {\text{ = }}{\left( {20} \right)^2}{\text{ = 400 units}} \cr
& \Rightarrow {\text{ Total compound interest }} \cr
& {\text{41 Units }} \to {\text{Rs. 410 }} \cr
& {\text{1 Units }} \to {\text{Rs. 10 }} \cr
& {\text{400 Units }} \to {\text{Rs. 400 }} \cr
& {\text{Total simple interest}} \cr
& {\text{ = Rs. 400}} \cr} $$
Alternate
Total compound interest for 2 years at 5% p.a.
$$\eqalign{
& {\text{ = 5 + 5 + }}\frac{{5 \times 5}}{{100}} = 10.25\% \cr
& {\text{Total simple interest}} \cr
& = 10\% \cr
& \Rightarrow 10.25\% \to 410 \cr
& \Rightarrow 10\% \to 400 \cr
& {\text{Simple interest}} \cr
& {\text{ = Rs}}{\text{. 400}} \cr} $$

Answer: Option C. -> Rs. 3200
For a first result cross check with option (Go with option (C) and check it.)
Principal is Rs. 3200
3200 of 5% for 1st year = 160
then, principal = 3200 + 160 = 3360
3360 of 5% for 2nd year = 168
∴ Interest = 160 + 168 = 328

Answer: Option C. -> 9 : 6 : 4
$$\eqalign{
& P{\left( {1 + \frac{R}{{100}}} \right)^5} = 150\% \,{\text{of }}P = \frac{3}{2}P \cr
& \Rightarrow {\left( {1 + \frac{R}{{100}}} \right)^5} = \frac{3}{2} \cr} $$
  $$x{\left( {1 + \frac{R}{{100}}} \right)^{10}} = y{\left( {1 + \frac{R}{{100}}} \right)^{15}} = $$       $$z{\left( {1 + \frac{R}{{100}}} \right)^{20}}$$
  $$ \Rightarrow x{\left\{ {{{\left( {1 + \frac{R}{{100}}} \right)}^5}} \right\}^2} = $$      $$y{\left\{ {{{\left( {1 + \frac{R}{{100}}} \right)}^5}} \right\}^3} = $$     $$z{\left\{ {{{\left( {1 + \frac{R}{{100}}} \right)}^5}} \right\}^4}$$
$$\eqalign{
& \Rightarrow x \times {\left( {\frac{3}{2}} \right)^2} = y \times {\left( {\frac{3}{2}} \right)^3} = z \times {\left( {\frac{3}{2}} \right)^4} \cr
& \Rightarrow \frac{{9x}}{4} = \frac{{27y}}{8} = \frac{{81z}}{{16}} = k({\text{say}}) \cr
& \Rightarrow x = \frac{{4k}}{9},y = \frac{{8k}}{{27}},z = \frac{{16k}}{{81}} \cr
& \Rightarrow x:y:z = \frac{{4k}}{9}:\frac{{8k}}{{27}}:\frac{{16k}}{{81}} \cr
& \Rightarrow x:y:z = 36:24:16 \cr
& \Rightarrow x:y:z = 9:6:4 \cr} $$

Answer: Option B. -> Rs. 7
Simple Interest (I) = $$\frac{{PTR}}{{100}}$$
350 = $$\frac{{P \times 2 \times 4}}{{100}}$$
P = 4375
C.I = 175 + 175 + 7 = 357
Difference = 357 - 350 = Rs. 7

Answer: Option D. -> Rs. 32000
$$\eqalign{
& {\text{Rate}} = 10\% ,\, \cr
& {\text{Let}}\,{\text{Principal}} = P \cr
& {\text{S}}{\text{.I}}{\text{.}} = \frac{{P \times 10 \times 3}}{{100}} = \frac{{3P}}{{10}} \cr
& {\text{C}}{\text{.I}}{\text{.}} = P\left\{ {{{\left( {1 + \frac{1}{{10}}} \right)}^3} - 1} \right\} \cr
& \Rightarrow {\text{C}}{\text{.I}}{\text{.}}\,\, - \,\,{\text{S}}{\text{.I}}{\text{.}} = 992 \cr
& \Rightarrow P\left\{ {{{\left( {1 + \frac{1}{{10}}} \right)}^3} - 1} \right\} - \frac{{3P}}{{10}} = 992 \cr
& \Rightarrow P\left\{ {{{\left( {\frac{{11}}{{10}}} \right)}^3} - 1 - \frac{3}{{10}}} \right\} = 992 \cr
& \Rightarrow P\left\{ {\frac{{\left( {1331 - 1000 - 300} \right)}}{{1000}}} \right\} = 992 \cr
& \Rightarrow P\left( {\frac{{31}}{{1000}}} \right) = 992 \cr
& \Rightarrow P = 32000 \cr} $$
Alternate:
Rate = 10% = $$\frac{1}{{10}}$$
Let principal ⇒ (10)3 = 1000
Interest 1st year → 100
Interest 2nd year → 100 + 10
Interest 3rd year = 100 + 10 + 10 + 1
C.I – S.I = 331 – 300 = 31
31 → 992
1 → 32
P → 32000

Answer: Option D. -> Rs. 8000
Let the sum be = 400x
Simple Interest = $$\frac{{PTR}}{{100}}$$
S.I = $$\frac{{400x \times 2 \times 5}}{{100}}$$ = 40x
for Compond Interest 5% = $$\frac{{1}}{20}$$
C.I = 20x + 20x + x = 41x
Difference = 41x - 40x = 20
i.e. x = 20
∴ Sum is = 400 × 20 = 8000

Answer: Option B. -> Rs. 500
Let the sum of money be rs. P
Then,
$$\eqalign{
& \Rightarrow \left[ {P{{\left( {1 + \frac{R}{{100}}} \right)}^t} - P} \right] = {\text{C}}{\text{.I}}{\text{.}} \cr
& \Rightarrow \left[ {P{{\left( {1 + \frac{{10}}{{100}}} \right)}^2} - P} \right] = 525 \cr
& \Rightarrow P{\left( {\frac{{11}}{{10}}} \right)^2} - 1 = 525 \cr
& \Rightarrow P\left( {\frac{{121}}{{100}} - 1} \right) = 525 \cr
& \Rightarrow P\left( {\frac{{21}}{{100}}} \right) = 525 \cr
& \Rightarrow P = \frac{{525 \times 100}}{{21}} \cr
& \Rightarrow P = {\text{Rs}}{\text{.}}\,2500 \cr
& \therefore {\text{ Sum of money}} \cr
& {\text{ = Rs}}{\text{. 2500}} \cr} $$
Simple interest on the same sum Rs. 2500 for 4 (double the time) years at 5% (half the rate of percent per annum) is
So,
$$\eqalign{
& {\text{S}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left( {\frac{{2500 \times 5 \times 4}}{{100}}} \right) \cr
& \,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 500}} \cr} $$

Answer: Option C. -> Rs. 306.04
In one year there are 4 quarterly months.
∴ 9 month = 3 quarter
New Rate of Interest = $$\frac{8}{4}$$   = 2%
i.e 2% = $$\frac{1}{50}$$
Total CI = (100 + 100 + 100) + (2 + 2 +2) + 0.04
             = Rs.306.04

Answer: Option B. -> Rs. 121