Given: The sum of money doubles itself in 5 years.

To find: In how many years will it become four fold (if interest is compounded)?

Let the sum of money be P.

After 5 years, the sum becomes 2P.

Let the time required to become four-fold be n years.

Using the formula for compound interest, we have:

A = P(1 + r/n)^(nt)

where A is the amount after n years, r is the rate of interest, and t is the time period.

Since the sum becomes four-fold, we have:

4P = P(1 + r/n)^(nt)

Dividing both sides by P, we get:

4 = (1 + r/n)^(nt)

Taking the logarithm of both sides, we get:

log 4 = log[(1 + r/n)^(nt)]

Using the property of logarithms, we can bring down the exponent:

log 4 = nt log(1 + r/n)

Solving for n, we get:

n = [log 4]/[t log(1 + r/n)]

Since the sum doubles in 5 years, we have:

2P = P(1 + r/n)^(5t)

Dividing both sides by P, we get:

2 = (1 + r/n)^(5t)

Taking the logarithm of both sides, we get:

log 2 = 5t log(1 + r/n)

Substituting this into the equation for n, we get:

n = [log 4]/[log 2/5 log(1 + r/n)]

Simplifying this expression, we get:

n = 10 log 2/log(1 + r/n)

Since we know that the sum doubles in 5 years, we can substitute this into the equation for n, and solve for r/n:

2 = (1 + r/n)^5

Taking the fifth root of both sides, we get:

1 + r/n = 2^(1/5)

Subtracting 1 from both sides, we get:

r/n = 2^(1/5) - 1

Substituting this into the equation for n, we get:

n = 10 log 2/log(2^(1/5))

Simplifying this expression, we get:

n = 10 log 2/[(1/5) log 2]

n = 10(5)

n = 50

Therefore, the sum of money will become four-fold in 50/5 = 10 years.

Hence, the correct answer is option (b) 10.