The ratio of the profit to the cost price of a product is 2: 7. What is the ratio of its selling price to its profit?

Correct — A. Write the ratio as amounts: CP = 7k and profit = 2k.

Selling price = CP + profit
= 7k + 2k = 9k

SP : profit = 9k : 2k
= 9 : 2 → option (a)

Why the others are wrong

• (b)
  9:10 — 9 : 10 puts the selling price below the profit. Since SP = CP + profit, SP is the larger number whenever the cost is positive, so the ratio must be above 1.
• (c)
  5:15 — 5 : 15 reduces to 1 : 3, a selling price one-third of the profit. SP = 7k + 2k = 9k is well above the profit of 2k, so a ratio below 1 cannot be right.
• (d)
  6:17 — 6 : 17 also has the selling price below the profit. With CP = 7k and profit = 2k, SP is 9k, four and a half times the profit, not about a third of it.

A ratio of profit to cost price fixes both amounts up to one multiplier k. Write them as 2k and 7k, and every other price follows by addition.

Selling price = cost price + profit, so SP = 9k. Any ratio among the three can then be read off: SP : CP = 9 : 7, CP : SP = 7 : 9, SP : profit = 9 : 2.

Key facts

• Selling price = cost price + profit, so SP : profit = (CP + profit) : profit.
• Profit : CP = 2 : 7 means a profit of 2⁄7 × 100 ≈ 28.57% on cost.
• When there is a profit, SP is larger than both CP and the profit.

Common traps

• Taking SP as 7k instead of 7k + 2k, which gives 7 : 2, the cost-to-profit ratio.
• Answering profit : SP = 2 : 9 when the question puts the selling price first.

No directly related past PYQ was found.