Answer: Option A. -> Rs.7500
Answer: (a)Using Rule 1Simple Interest (S.I.)= ${\text"Principal × Rate × Time"/100$ orS.I. = ${\text"P × R × T"/100$P = ${\text"S.I." × 100}/\text"R × T"$, R = ${\text"S.I." × 100}/\text"P × T"$, T = ${\text"S.I." × 100}/\text"P × R"$ A = P + S.I. or S.I. = A - P

Answer: Option D. -> 4%
Answer: (d)Principal + S.I. for $5/2$ years = Rs.1012 ...(i)Principal + S.I. for 4 years = Rs.1067.20 ...(ii)Subtracting equation (i) from (ii)S.I. for $3/2$ years = Rs.55.20S.I. for $5/2$ years= $55.20 × 2/3 × 5/2$ = Rs.92Principal= Rs.(1012 - 92) = Rs.920Rate = ${92 × 100}/{920 × 5/2}$= ${2 × 92 × 100}/{920 × 5}$ = 4%Using Rule 12,R = $({A_1 - A_2}/{A_2T_1 - A_1T_2})$ × 100= $({1012 - 1067.20}/{1067.20 × 5/2 - 1012 × 4}) × 100$= ${- 55.2}/({2668 - 4048}) × 100$= ${- 55.2}/{- 1380} × 100$ = 4%

Answer: Option A. -> Rs.600
Answer: (a)Principal + SI for 2 years = Rs.720 .... (i)Principal + SI for 7 years = Rs.1020 .....(ii)Subtracting equation (i) from (ii) get,SI for 5 years= Rs.(1020 - 720) = Rs.300SI for 2 years= Rs.300 × $2/5$ = Rs.120Principal = Rs.(720 - 120) = Rs.600Using Rule 12,P = $({A_2T_1 - A_1T_2}/{T_1 - T_2})$= $({1020 × 2 - 720 × 7}/{2 - 7})$= $({2040 - 5040}/{- 5})$= ${- 3000}/{- 5}$ = Rs.600

Answer: Option C. -> 6%
Answer: (c) P + S.I. for 5 years = 5200 ..(i)P + SI for 7 years = 5680 ...(ii)On subtracting equation (i) from (ii),SI for 2 years = 480SI for 1 year = Rs.240From equation (i),P + 5 × 240 = 5200P = 5200 - 1200 = Rs.4000R = ${SI × 100}/{T × P}$= ${240 × 100}/{1 × 4000}$ = 6% Using Rule 12If certain sum P amounts to Rs. $A_1$ in $t_1$ years at rate of R% and the same sum amounts to Rs. $A_2$ in $t_2$ years at same rate of interest R%. Then,(i) R = $({A_1 - A_2}/{A_2T_1 - A_1T_2})$ × 100(ii) P = $({A_2T_1 - A_1T_2}/{T_1 - T_2})$

Answer: Option A. -> Rs.44000
Answer: (a)Using Rule 1Simple Interest (S.I.)= ${\text"Principal × Rate × Time"/100$ orS.I. = ${\text"P × R × T"/100$P = ${\text"S.I." × 100}/\text"R × T"$, R = ${\text"S.I." × 100}/\text"P × T"$, T = ${\text"S.I." × 100}/\text"P × R"$ A = P + S.I. or S.I. = A - P

Answer: Option A. -> 3 years
Answer: (a)Using Rule 1,Time = $\text"S.I. × 100"/ \text"Principal × Rate"$= $3/10 × 100/10$ = 3 years

Answer: Option A. -> 3 : 2
Answer: (a)Using Rule 1,Let the sum of x be lent at the rate of 4% and (5000 - x) at the rate of 5%${x × 4 × 2}/100 + {(5000 - x) × 5 × 2}/100$ = 4408x + 50000 - 10x = 440002x = 50000 - 44000 = 6000x = Rs.3000Rs.(5000 - x) = Rs.(5000 - 3000) = Rs.2000Now, Required ratio= 3000 : 2000 = 3 : 2

Answer: Option D. -> Rs.2400
Answer: (d)Principal lent at 8% S.I. = Rs.x.Principal lent at 10% S.I. = Rs.(4000 - x)S.I. = $\text"Principal × Time × Rate"/100$${x × 8}/100 + {(4000 - x) × 10}/100$ = 3528x + 40000 - 10x = 352002x = 40000 - 35200 = 4800x = $4800/2$ = Rs.2400

Answer: Option C. -> 25 : 2
Answer: (c)Required ratio = 5 : $2/5$ = 25 : 2$\text"loan amount"/ \text"Interest amount" = 5/2$Interest rate = $2/5$[Since, ${P + I}/I = 5/2 ⇒ P/I + I = 5/2$⇒ $P/I = 3/2, then I = 2/5$]$ \text"loan amount"/ \text"Interest rate"$= $5/{2/5}= 25/2$ or 25 : 2

Answer: Option B. -> 2 : 1
Answer: (b)Using Rule 1,First part = Rs. x and second part= (12000 - x )${x × 3 × 12}/100 = {(12000 - x) × 9 × 16}/200$$x/{12000 - x} = {9 × 16 × 100}/{3 × 12 × 200}$= $2/1$ = 2 : 1