Ram had ₹ 1000 in his Savings Bank Account. Every month in the first week he needs money, so he withdraws ₹ 500, but by the end of the month, he deposits ₹ 750. After how many months the original amount will grow three times?

### Concept & Logic This problem requires tracking a monthly balance with sequential deductions and additions. You must find the net change over a full month and use it to determine when a fixed final threshold is reached at the end of a cycle. ### Step-by-Step Solution * **Given:** * Initial balance = ₹ 1000 * Target balance = $3 \times 1000 =$ ₹ 3000 * Monthly withdrawal = ₹ 500 * Monthly deposit = ₹ 750 * **Deduction:** Find the net monthly growth after a full cycle (withdrawal + deposit). $$\text{Net Monthly Increase} = 750 - 500 = ₹ 250$$ We need to find the number of months $m$ it takes to reach ₹ 3000 at the end of a month. * **Calculation:** After $m$ months, the balance at the end of the month is expressed as: $$\text{Balance} = 1000 + 250m$$ Set the equation to reach the target balance: $$1000 + 250m = 3000$$ $$250m = 2000$$ $$m = 8$$ Let's verify the 8th month: Start of month 8 balance = ₹ 2750. First week withdrawal = $2750 - 500 =$ ₹ 2250. End of month deposit = $2250 + 750 =$ ₹ 3000. Target reached perfectly. ### Exam Strategy & Shortcut Simply use the net monthly gain as a linear rate. $\text{Required Growth} = 3000 - 1000 = 2000$. Since each month ends with a net $+250$, divide the required growth by the net gain: $2000 \div 250 = 8$. ### Common Pitfall Applying the "monkey climbing" logic (where the target might be hit mid-cycle). Here, the negative action (withdrawal) happens *first*, causing a mid-month dip, and the positive peak happens *last* with the deposit. Thus, the target is hit at the end of the month, and standard linear rate division works without needing to adjust for an early threshold cross. ### Final Answer **Therefore, the correct answer is 8 months.**