Sunil has Rs 450 in her savings account . she deposits Rs 40 each month. Arun has Rs 975 in his checking account. He writes a check for Rs 45.90 each month for his cell phone bill. He also writes a check for Rs 19.55 each month for his water bill. After how many months will Sunil and Arun have the same amount of money in their accounts ?

The correct answer is: After approximately 5 months (4.98 months) the balance in Sunil's and Arun's Account would be the same.

Step-by-step solution:-
Let x be the number of months after which balance in Sunil's and Arun's Account would be the same.
∴ As per the first condition,
Amount in Sunil's Account after x months = Initial Amount +/- Transactions made during each month * Number of months
∴ Amount in Sunil's Account after x months = 450 + 40 * x ..................................... (As per given information)
∴ Amount in Sunil's Account after x months = 40x + 450 ......................................... (Equation i)
Noe, As per the second condition,
Amount in Arun's Account after x months = Initial Amount +/- Transactions made during each month * Number of months
∴ Amount in Arun's Account after x months = 975 - (45.9 + 19.55) * x ..................................... (As per given information)
∴ Amount in Arun's Account after x months = 975 - 65.45x
∴ Amount in Arun's Account after x months = -65.45x + 975 ......................................... (Equation ii)
Since we need to find the value of x for which Balances in Sunil's and Arun's Account would be the same-
We Equate Equations i & ii-
40x + 450 = -65.45x + 975
∴ 40x + 65.45x = 975 - 450
∴ 105.45x = 525
∴ x = 525/ 105.45
∴ x ≈ 5
Final Answer:-
∴ After approximately 5 months (4.98 months) the balance in Sunil's and Arun's Account would be the same.