Riya deposits Rs. X in Fund A, which pays simple interest at 20% per year. At the end of one year, she withdraws the full amount and puts 95% of it into Fund B, which earns compound interest at 20% per year for one year. The difference between the interest earned from the two funds is Rs. 700. Find X.

The correct answer is Rs. 25,000.

Let us break down the problem step-by-step to calculate the value of X.

Step 1: Calculate the interest and total amount from Fund A
Initial principal deposited in Fund A = X
Rate of simple interest = 20% per year
Time period = 1 year

The simple interest earned from Fund A (I_A) is given by the formula:

$I_A=\frac{P\times R\times T}{100}$

Substituting the given values:

$I_A=\frac{X\times 20\times 1}{100}=0.20X$

The total accumulated amount at the end of 1 year in Fund A (A₁) is:

Step 2: Calculate the deposit and interest earned from Fund B
Riya withdraws the full amount of 1.20X and puts 95% of it into Fund B.
Principal deposited in Fund B (P_B):

$P_B=95\%\text{ of }1.20X=0.95\times 1.20X=1.14X$

Fund B earns compound interest at 20% per year for 1 year.
For a period of 1 year, compound interest is equal to 20% of the principal deposited in Fund B.
Interest earned from Fund B (I_B):

$I_B=20\%\text{ of }1.14X=0.20\times 1.14X=0.228X$

Step 3: Solve for X using the given difference in interest
The difference between the interest earned from Fund B and Fund A is Rs. 700:

$I_B-I_A=700$

Substitute the values of I_A and I_B into the equation:

$0.228X-0.20X=700$

$0.028X=700$

Solving for X:

$X=\frac{700}{0.028}$

$X=\frac{700000}{28}=25000$

Therefore, the value of X is Rs. 25,000.