A discount series of 10% and 16% on an invoice is the same as a single discount of:

Correct — A. Take the invoice as ₹100 and apply the two discounts in sequence.

After 10%: 100 × 0.90 = ₹90
After 16% on that ₹90: 90 × 0.84 = ₹75.60

Total taken off = 100 − 75.60 = ₹24.40, i.e. 24.4% → option (a)

By formula: 10 + 16 − (10 × 16)⁄100 = 26 − 1.6 = 24.4%.

Why the others are wrong

• (b)
  23.4% — 23.4% is 26 − 2.6. The amount to subtract from 26 is the product of the two rates over 100, 10 × 16 ⁄ 100 = 1.6, and 2.6 comes from nowhere in the data.
• (c)
  21.4% — 21.4% subtracts 4.6 from 26. Test it against the ₹100 invoice: the price falls to ₹90, then to ₹75.60, so ₹24.40 is gone, not ₹21.40.
• (d)
  22.4% — 22.4% is 26 − 3.6. Neither 10% nor 16% generates 3.6; the cross term for this pair is 1.6, which is why the answer sits just under 26.

Successive discounts multiply the surviving fraction, they do not add.

Ten per cent off leaves 0.90 of the price; sixteen per cent off that leaves 0.84 of what remains. Together 0.90 × 0.84 = 0.756, so 75.6% survives and 24.4% is the single equivalent discount.

The shortcut a + b − ab⁄100 is the same statement rearranged. The subtracted term ab⁄100 exists because the second discount is charged on an already reduced price, so it is worth less than its face rate.

The equivalent single discount is therefore always a little less than the sum of the parts.

Key facts

• Successive discounts multiply the remaining fractions: 0.90 × 0.84 = 0.756.
• The single equivalent discount for a% then b% is a + b − ab⁄100.
• For 10% and 16% that is 10 + 16 − 1.6 = 24.4%.
• The order of the two discounts does not change the result.

Common traps

• Adding the rates to 26% and stopping there.
• Charging the second discount on the original invoice rather than on the reduced amount.
• Flipping the sign of the cross term and answering 27.6%.

No directly related past PYQ was found.