Allocations and remaining balance: After spending 40% on machinery, 25% on building, 15% on raw material, and 5% on furniture, Hari Lal has ₹1305 left. What was the initial amount?

Introduction / Context:Multiple fixed-percentage expenditures reduce the initial amount to a final balance. Sum the percentages to find the remaining fraction of the original and then recover the starting amount from the final balance.

Given Data / Assumptions:

• Expenditures: 40% + 25% + 15% + 5% = 85% of the initial sum.
• Remaining = 15% of the initial sum.
• Final balance = ₹1305.

Concept / Approach:If S is the initial amount, remaining = 0.15S. Set 0.15S = 1305 and solve for S. Ensure percentages are applied on the same base (the original) since these are independent allocations stated as parts of the whole.

Step-by-Step Solution:Remaining fraction = 100% − 85% = 15% = 0.150.15S = 1305 ⇒ S = 1305 / 0.15 = 8700

Verification / Alternative check:Check: 15% of 8700 = 1305, so expenditures sum to 7395, consistent with the stated percentages totaling 85%.

Why Other Options Are Wrong:6500, 7225, 1390, 7800 do not yield ₹1305 as exactly 15%.

Common Pitfalls:Sequentially applying percentages (compounding) when the problem describes allocations as fractions of the original total; here they are parts of one whole.

Final Answer:Rs. 8700