An investor, invested ₹2,00,000 in shares. The shares rose by 18% on the first day, fell by 15% on the second day, and then fell by 3% on the third day. What is the net percentage increase or decrease in the value of the investor's shares? (Rounded up to one decimal place)

Correct — B. Chain the three multipliers rather than adding the percentages.

Day 1, up 18%: factor 1.18
Day 2, down 15%: factor 0.85
Day 3, down 3%: factor 0.97

1.18 × 0.85 = 1.003
1.003 × 0.97 = 0.97291

The holding ends at 0.97291 of its start, a fall of 1 − 0.97291 = 0.02709 = 2.709%, which to one decimal place is a decrease of 2.7% → option (b)

Why the others are wrong

• (a)
  increase by 2.7% — The size is right and the direction is wrong. The product 1.18 × 0.85 × 0.97 = 0.97291 sits below 1, so the shares close lower than they opened.
• (c)
  decrease by 2.2% — A fall of 2.2% would need a net multiplier of 0.978. The three factors actually multiply to 0.97291, giving 2.709%, which rounds to 2.7 and not to 2.2.
• (d)
  increase by 2.2% — Wrong on both counts. The net multiplier 0.97291 is under 1, so the movement is a fall, and its size is 2.709%, not 2.2%.

Successive percentage changes multiply; they do not add.

A rise of r% is a factor of (1 + r⁄100) and a fall of r% a factor of (1 − r⁄100). Applying three changes in turn means multiplying the three factors, because each change acts on the value left by the one before it.

Adding here would give 18 − 15 − 3 = 0 and the false conclusion that the investor broke even. The true close is 2,00,000 × 0.97291 = ₹1,94,582, a loss of ₹5,418.

Key facts

• Successive percentage changes multiply, so a rise of r% is a factor of (1 + r⁄100).
• 1.18 × 0.85 × 0.97 = 0.97291, a net fall of 2.709%.
• On ₹2,00,000 that leaves ₹1,94,582, a loss of ₹5,418.
• Adding the changes gives 18 − 15 − 3 = 0, which would wrongly report no change at all.

Common traps

• Adding the three percentages to zero and concluding the investment broke even.
• Applying the second and third changes to the original ₹2,00,000 instead of to the running value.
• Assuming the order of the changes matters — it does not, though the base at each step does change.

No directly related past PYQ was found.