Selling Price = 500 × 80/100 = Rs. 400. If profit is 25%, then CP = 400 × 100/125 = Rs. 320

Combined rate = 1/12 + 1/15 = 5/60 + 4/60 = 9/60 = 3/20. Time = 20/3 = 6.67 hours

Distance covered = 250 + 150 = 400m. Speed = 400/20 = 20 m/s = 20 × 18/5 = 72 km/h

Downstream speed = 12 + 3 = 15 km/h. Time = 60/15 = 4 hours

Let original number be x. x × 60/100 = 300. x = 300 × 100/60 = 500

Selling Price = 2500 × 92/100 = Rs. 2300

Number = 45 × 100/15 = 300. 40% of 300 = 300 × 40/100 = 120

# Solution: Net Percentage Change After Two Operations

When a quantity undergoes successive percentage changes, we apply each change sequentially to find the overall effect.

Step 1: Represent the original number

Let the original number be \(x\).

Step 2: Apply the 25% increase

After a 25% increase:

Step 3: Apply the 20% decrease

The decrease is applied to the new value \(1.25x\), not the original:

Step 4: Calculate the net change

The final value equals the original value. Therefore:

Assume the original number is 100.

Increase by 25%:

100×1.25=125

Then decrease by 20%:

125×0.80=100

So, the final value is again 100.

Therefore, the net percentage change is 0%.

Answer: The net percentage change is 0% (Option A)

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Key Insight: A 25% increase followed by a 20% decrease does NOT cancel out to 0% by simple arithmetic (25 − 20 = 5). Instead, multiplying the multipliers \((1.25 \times 0.80 = 1.00)\) gives the true result because the 20% decrease applies to the larger amount.

SP = CP + Profit = 500 + (35% of 500) = 500 + 175 = Rs. 675

A's work rate = 1/20, B's work rate = 1/30. Combined rate = 1/20 + 1/30 = 5/60 = 1/12. Time = 12 days