A dealer sets the marked price of a television 20% higher than its cost price. If he gives a discount of 15% and makes a profit of ₹300, what is the cost price of the television?

Correct — C.
Marked price = CP + 20% of CP = 1.2 CP
Selling price after 15% off = 0.85 × 1.2 CP = 1.02 CP
Profit = 1.02 CP − CP = 0.02 CP

Set the profit to ₹300: 0.02 CP = 300
CP = 300 ÷ 0.02 = ₹15,000 → option (c).

Check: MP = ₹18,000, SP = ₹15,300, profit = ₹300.

Why the others are wrong

• (a)
  ₹10,000 — ₹10,000 gives a profit of ₹200. Marked at ₹12,000 and sold at 15% off for ₹10,200, it earns 2% of cost, which is ₹200, not ₹300.
• (b)
  ₹12,500 — ₹12,500 gives a profit of ₹250. It is marked at ₹15,000 and sold for ₹12,750. The profit is always 2% of cost, so ₹300 needs a cost of ₹15,000.
• (d)
  ₹18,000 — ₹18,000 is the marked price, not the cost. A cost of ₹18,000 would be marked at ₹21,600, sold for ₹18,360, and earn ₹360.

A markup and a discount multiply; they do not add. A 20% markup followed by a 15% discount leaves 1.2 × 0.85 = 1.02 times the cost, a net gain of 2%.

Once the net effect is one percentage of cost, the rupee profit fixes the cost directly: 2% of CP = ₹300.

Netting 20 − 15 = 5% goes wrong because the 15% is taken on the marked price, not on cost.

Key facts

• SP = CP × (1 + markup %) × (1 − discount %).
• A 20% markup and a 15% discount give SP = 1.02 × CP, a 2% profit.
• Here MP = ₹18,000 and SP = ₹15,300.

Common traps

• Netting 20% − 15% = 5% and solving 5% of CP = ₹300, which gives ₹6,000.
• Stopping at the marked price, ₹18,000, when the stem asks for the cost price.

No directly related past PYQ was found.