A person first increases the price of a commodity by 8% and then he announces a discount of 18%. The actual discount (in%) on the original price is:

Correct — D. Work on a base price of ₹100.

Raise it 8%: 100 × 1.08 = 108
The 18% discount is announced on that raised price: 18% of 108 = 19.44
Selling price = 108 − 19.44 = 88.56
Actual discount on the original = 100 − 88.56 = 11.44% → option (d)

Shortcut: net change = 8 − 18 − (8 × 18)⁄100 = 8 − 18 − 1.44 = −11.44%.

Why the others are wrong

• (a)
  8.44 — 8.44 implies a selling price of ₹91.56, i.e. only ₹16.44 off the raised ₹108. That is a 15.2% cut, not the 18% announced.
• (b)
  14.44 — 14.44 implies a selling price of ₹85.56. The discount actually removes ₹19.44, of which ₹8 merely cancels the earlier raise, leaving 11.44 below the original ₹100.
• (c)
  9.44 — 9.44 implies a selling price of ₹90.56, which is only ₹17.44 off the raised ₹108. The announced 18% of 108 is ₹19.44, so the price falls further.

Successive percentage changes multiply, they do not add, because the second change acts on a base the first change has already moved.

Here the 18% discount is taken on ₹108, not on ₹100, so it removes ₹19.44 rather than ₹18. Eight of those rupees only undo the raise, and ₹11.44 is what the buyer actually saves against the original price.

In factor form: 1.08 × 0.82 = 0.8856, so 88.56% of the original price is paid and 11.44% is the real discount.

Key facts

• Successive changes of x% and y% combine to x + y + xy⁄100 percent, a decrease entered as negative.
• +8% then −18% gives 8 − 18 − 1.44 = −11.44%.
• A raise of 8% followed by a discount of 18% leaves 1.08 × 0.82 = 0.8856 of the original price.

Common traps

• Subtracting the percentages, 18 − 8 = 10, which ignores that the discount falls on the raised price.
• Charging the 18% on the original ₹100 instead of on ₹108.
• Reporting the cut as a percentage of the raised price, when the stem asks for it on the original.

No directly related past PYQ was found.