If, on a marked price, the difference between selling prices with a discount of 65% and with two successive discounts of 30% and 40% is ₹105, then the marked price (in ₹) is:

Correct — A. Turn each scheme into a multiplier on the marked price M.

One discount of 65%: SP = (1 − 0.65)M = 0.35M
30% then 40%: SP = 0.70 × 0.60 × M = 0.42M

Difference = 0.42M − 0.35M = 0.07M
0.07M = 105
M = 105 ⁄ 0.07 = ₹1,500 → option (a)

Check: 0.42 × 1500 = 630 and 0.35 × 1500 = 525, and 630 − 525 = 105.

Why the others are wrong

• (b)
  1,050 — 7% of ₹1,050 is ₹73.50, not ₹105. The figure ₹105 happens to be 10% of 1,050, which is what makes this option look right at a glance.
• (c)
  1,650 — 7% of ₹1,650 is ₹115.50, ten and a half rupees more than the difference the question fixes.
• (d)
  1,320 — 7% of ₹1,320 is ₹92.40, short of ₹105 by more than twelve rupees.

A discount of d% multiplies the price by (1 − d⁄100), and successive discounts multiply rather than add.

30% then 40% leaves 0.70 × 0.60 = 0.42 of the marked price, so the equivalent single discount is 58%, not 70%. A single 65% discount leaves 0.35.

The gap between the two schemes is therefore a fixed 7% of the marked price, whatever that price happens to be, and the rupee difference converts straight into M.

Key facts

• Successive discounts of a% and b% leave (1 − a⁄100)(1 − b⁄100) of the marked price.
• The equivalent single discount for a% then b% is a + b − ab⁄100.
• Discounts of 30% and 40% together equal a single discount of 58%.
• The two schemes in this question differ by exactly 7% of the marked price.

Common traps

• Adding 30% and 40% into 70% and comparing that against 65%.
• Matching the ₹105 to the option 1,050 because it reads like a clean 10%.

No directly related past PYQ was found.