-   Interest on Rs. 100 for the year = Rs. 4   Interest on Rs. 100 for the second year      = 100   (  1+ 4  ) 2 - 1 100    - 4                = Rs. 4.16     Now if Rs. 4.16 - Rs. 4 = Rs. 0.16 is the difference then principal = Rs. 100   Now if Rs. 88 is the difference then principal = 100 x 88  = Rs. 55,000             16      

Let the sum of money lent be "P". Then, the interest earned for the first year is given by P * 4/100 = 0.04P.

For the second year, the interest earned is given by P * (4/100)^2 = 0.00016P.

The difference in interest between the second and first year is given as Rs. 88. Therefore, we have:

0.00016P - 0.04P = 88

Simplifying the above equation, we get:

0.04P(1 - 0.04) = 88

0.96P = 88

P = 88/0.96 = 55000

Hence, the sum of money lent is Rs. 55000, which corresponds to option B.

In summary, the solution to the problem involves the following steps:

• Let the sum of money lent be "P".
• Use the formula for calculating compound interest to find the interest earned for the first year: P * 4/100 = 0.04P.
• Use the same formula to find the interest earned for the second year: P * (4/100)^2 = 0.00016P.
• Calculate the difference in interest between the second and first year: 0.00016P - 0.04P = 88.
• Simplify the equation to get P = 55000, which is the sum of money lent.

If you think the solution is wrong then please provide your own solution below in the comments section .