Shortcut Trick
Net percentage change = a + b + (ab ÷ 100)
Here, a = −10% and b = +12%
Net % change = −10 + 12 + [(−10 × 12) ÷ 100] = 2 − 1.2 = 0.8% (increase)
Final Value = 62,000 + 0.8% of 62,000 = 62,000 + 496 = 62,496
∴ The correct answer is ₹62,496.
Alternate Method
Given:
Initial Investment = ₹62,000
First year decrease = 10%
Second year increase = 12%
Calculations:
⇒ Value after 1st Year = 62,000 − (10% of 62,000)
⇒ Value after 1st Year = 62,000 − 6,200 = ₹55,800
⇒ Value after 2nd Year = 55,800 + (12% of 55,800)
⇒ 12% of 55,800 = (12 ÷ 100) × 55,800 = 12 × 558 = 6,696
⇒ Final Value = 55,800 + 6,696 = ₹62,496
∴ The correct answer is ₹62,496.
Additional Information
Successive Percentage Change
When a value changes by x% and then y%, the effective change is (x + y + xy/100)%. This is also applicable to Compound Interest calculations.
Multiplying Factor Method
For an x% increase, multiply by (1 + x/100). For an x% decrease, multiply by (1 − x/100). In this case: 62000 × 0.90 × 1.12.
Commutative Property of Change
The final value remains the same regardless of the order of percentage changes (i.e., 12% increase followed by 10% decrease yields the same result).