Option 3 : 56 years

__Shortcut Trick__

If a sum of money becomes ‘n_{1}’ times in 'T_{1}’ years and 'n_{2}’ times in 'T_{2}’ years at simple interest, then

(n_{1} - 1)/(n_{2} - 1) = (T_{1})/(T_{2})

(2 - 1)/(8 -1) = (8)/(T_{2})

⇒ 1/7 = (8)/(T2)

⇒ T2 = 56 years

∴ The time taken to 8 times the amount is 56 years.

**Given:**

Amount = 2P

Time = 8 years

Formula Used:

S.I = (PRT/100) + P

Amount = S.I + P

Where,

S.I = Simple interest

P = Principal

R = Rate of interest

T = Time duration

Calculation:

Let the principal be P

⇒ S.I = 2P - P

⇒ S.I = P

According to the question, we have

P = (P × R × 8)/100

⇒ R = 100/8

⇒ R = 12.5%

Now, the principal increase 8 times itself

S.I = 8P - P

⇒ S.I = 7P

7P = (P × 12.5 × T)/100

⇒ 7 = T/8

⇒ T = 8 × 7

⇒ T = 56 years

**∴ The time taken to 8 times the amount is 56 years.**

__Alternate Method__

Interest = 2P - P

⇒ P = 100% of principle

Time = 8 years

Rate = Interest/Time

⇒ 100/8 = 12.5%

New interest = 8P - P

⇒ 7P = 700% of principle

Time = Interest/Rate

⇒ 700/12.5

⇒ 56 Years

∴ The time taken to 8 times the amount is 56 years.