A woman sold a typewriter for Rs 13718 in the system of compound depriciation at the rate of 5 percent .If she had purchased it 3 years before how much did she pay for it by that time?

Rs 16000

Step-by-step explanation:

Given that :

Price at which typewriter was sold = Rs 13718

Compound Depreciation rate = 5%

Time = 3 years

Amount paid for typewriter 3 years ago

Using the relation :

Final amount = Initial amount(1 - r/n)^nt

n = number of compounding times per period

Rate = r = 5% = 0.05

t = time

A = Final amount = 13718

Initial amount = original purchase price (p)

Therefore ;

13718 = p(1 - 0.05)^3

13718 = p(0.95)^3

13718 = p * 0.857375

13718 = 0.857375p

p = 13718 / 0.857375

P = Rs 16000

Amount paid at the time of purchase = 16000

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents