Maths-

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Question

# 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 ?

Hint:

### Account Balance after x months = Initial Amount +/- Transactions made during each month × Number of months

## 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.

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