Answer: Option A. -> 12.5%
Answer: (a)Principal = Rs.xAmount = Rs.2x Interest = 2x - x = Rs.xRate = ${SI × 100}/\text"Principal × Time"$= ${x × 100}/{x × 8} = 25/2$ = 12.5 % per annumUsing Rule 3,R % = ${(n - 1)}/T × 100%$= ${(2 - 1)}/8 × 100%$ = 12.5%

Answer: Option C. -> 12$1/2$%
Answer: (c)Let principal be Rs. x.Amount = Rs.2xInterest = Rs.(2x - x) = Rs.xRate = ${S.I. × 100}/\text"Principal × Time"$= ${x × 100}/{x × 8} = 25/2$= 12$1/2%$ per annum

Answer: Option B. -> 16 years
Answer: (b)According to the question,If principal be Rs. x, thenS.I. = Rs. xTime = ${SI × 100}/\text"Principal × Rate"$= ${x × 100}/{x × 25/4} = 400/25$ = 16 yearsUsing Rule 3,T = ${(n - 1)}/R × 100%$= ${2 - 1}/{25/4} × 100$= $400/25$ = 16 years.

Answer: Option D. -> 30 years
Answer: (d)Let the principal be x.Case-I$2x = {x × R × 15}/100$R = ${2 × 100}/15 = 40/3%$Case-IISI = 4x$4x = {x × 40 × T}/300$T = ${4 × 300}/40 = 30$ yearsUsing Rule 3,R = ${(3 - 1)}/15 × 100%$= $2/15 × 100%$= $2/3 × 20% = 40/3%$T = ${(n - 1)}/R$ Years= ${(5 - 1)}/{40/3} × 100$ = 30 years.

Answer: Option D. -> 16 years
Answer: (d)TIme = ${SI × 100}/\text"Principal × Rate"$= ${x × 100}/{x × 25/4}$ = 16 yearsUsing Rule 3,T = ${(n - 1)}/{R%} years$= ${(2 - 1)}/{25/4} × 100$ years = 16 years.

Answer: Option B. -> 5$5/9$%
Answer: (b)Principal = PAmount = ${7p}/6$S.I. = ${7p}/6 - P = P/6$R = ${S.I × 100}/{P × T} = {P × 100}/{6 × p × 3}$= $50/9 = 5{5}/9%$Using Rule 3If a certain sum becomes 'n' times of itself in T years on Simple Interest, then the rate per cent per annum is.R% = ${(n - 1)}/T × 100%$ andT = ${(n - 1)}/R × 100%$

Answer: Option C. -> 2 years
Answer: (c)Principal = Rs.P and time = T yearsS.I. = $\text"Principal × Time × Rate"/100$According to the question,P + ${PT × 5}/100$ = 2200P + ${PT}/20$ = 2200 ...(i)Again, ${PT × 8}/100 - {PT × 5}/100$= 2320 - 2200${3PT}/100$ = 120PT = ${120 × 100}/3$ = 4000 ...(ii)From equation (i),P + $4000/20$ = 2200P = 2200 - 200 = Rs. 2000From equation (ii),PT = 4000T = $4000/2000$ = 2 yearsAlternative MethodDifference in rates= 8 - 5 = 3%Since,3% ≡ 2320 - 2200 = 1205% ≡ $120/3$ × 5 = 200Principal = Rs.(2200 - 200) = Rs.2000Time = ${200 × 100}/{2000 × 5}$ = 2 years

Answer: Option A. -> Rs.8,250
Answer: (a)Using Rule 1,SI = Rs.(7200–6000) = Rs.1200SI = $\text"PRT"/100$1200 = ${6000 × R × 4}/100$R = ${1200 × 100}/{6000 × 4}$ = 5%New rate of R = 5×1.5 = 7.5%Then, SI = ${6000 × 7.5 × 5}/100$ = Rs.2250Amount = Rs.(6000 + 2250) = Rs.8250

Answer: Option D. -> 6%
Answer: (d)According to the question,Principal = Rs.x.Interest = Rs.x.Time = $50/3$ yearsRate = ${Interest × 100}/\text"Principal × Time"$= ${x × 100}/{x × {50/3}}$= ${100 × 3}/50$ = 6% per annum

Answer: Option B. -> 10%
Answer: (b)Let the principal be Re.1S.I. = $41/40 - 1 = 1/40$Now, rate = ${\text"Interest" ×100}/{\text"Principal × Time"}$= ${1/40 × 100}/{1 × 1/4} = {100 × 4}/40$ = 10%Using Rule 3,R = ${(41/40 - 1) × 100%}/{1/4}$= $1/40 × 4 × 100%$ = 10%