Alipta got some amount of money from her father. In how many years will the ratio of the money and the interest obtained from it be 10 : 3 at the rate of 6 % simple interest per annum ?

Options

A. 7 years
B. 3 years
C. 5 years
D. 4 years

Answer

To solve the problem step by step, let's denote:

- Principal amount (the money Alipta received) = P
- Rate of interest = 6% per annum
- Time in years = T
- Simple Interest (SI) = P * R * T / 100, where R is the rate of interest.

According to the problem, the ratio of the money (P) to the interest (SI) is given as 10:3. This can be expressed mathematically as:

\[ \frac{P}{SI} = \frac{10}{3} \]

Step 1: Express Simple Interest in terms of Principal, Rate, and Time.

The formula for Simple Interest is:

\[ SI = \frac{P \times R \times T}{100} \]

Substituting the rate R = 6% into the formula gives:

\[ SI = \frac{P \times 6 \times T}{100} \]

Step 2: Substitute SI in the ratio equation.

Now, substituting SI in the ratio equation:

\[ \frac{P}{\frac{P \times 6 \times T}{100}} = \frac{10}{3} \]

Step 3: Simplify the equation.

This simplifies to:

\[ \frac{P \times 100}{P \times 6 \times T} = \frac{10}{3} \]

Cancelling P from both sides (assuming P ≠ 0):

\[ \frac{100}{6T} = \frac{10}{3} \]

Step 4: Cross-multiply to solve for T.

Cross-multiplying gives:

\[ 100 \times 3 = 10 \times 6T \]

This simplifies to:

\[ 300 = 60T \]

Step 5: Solve for T.

Now, divide both sides by 60:

\[ T = \frac{300}{60} = 5 \]

So, the time T is 5 years.

**Final Answer: Alipta will have the ratio of money to interest as 10:3 in 5 years.**

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