Question

a sum of rupees 7000 amounts to rupees 8260 in 3 years at a certain rate of interest in what time will rupees 5000 amount to Rupees 6500 at the same rate of interest​

Answer 1

5 years

given principal (P) =7000

simple interest (SI)=8260-7000

SI =1260

time (T) =3 years

rate (R) =(SI×100)/(T×P)

R=(1260×100)/(3×7000)

R=6%

for same rate of interest time T = ?

given principal P =5000

simple interest SI=6500-5000

SI =1500

time T=(SI×100)/(P×R)

time T=(1500×100)/(5000×6)

time T=5 years

Answer 2

Answer:

If we consider it is a case of simple interest then

Interest for 3 years = 8260 - 7000 = 1260

Interest for 1 year = 1260/3 = 420

Rate if interest = (420/7000) * 100 = 6%

For Rs. 5000 becomes Rs. 6500,

the interest = 6500 - 5000 = 1500

The rate is 6%

Yearly interest = 5000 * 6/100 = 300

No. of years = 1500/300 = 5 Ans

For compound interest, let the rate is r

7000 * ( 1 + r/100)^3 = 8260

Or, (1 + r/100)^3 = 8260/7000 = 1.18

Or, 1 + r/100 = 1.18^(1/3) = 1.05672

Or, r = (1.05672 - 1) * 100 = 5.672%

For Rs. 5000 becoming Rs. 6500, let the number of years = x

So, 5000 * (1.05672)^x = 6500

Or, (1.05672)^x = 6500/5000 = 1.3

Taking log and solving, x log 1.05672 = log 1.3

Or x = log 1.3 / log 1.05672 = 0.1139/0.02396

Or x = 4.75 years Ans.

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