Explanation:

Let’s break this one down step by step, in plain English:

- Type X articles:

- Cost price : Marked price = 8 : 15 ? Let’s say cost is 8k, marked is 15k, k is some multiplier.

- Selling price is less than marked price (because discount), but you earn profit.

- Total revenue from 600 X = Rs. 75,000, so per article revenue (selling price) = 75,000 / 600 = Rs. 125.

- Type Y articles:

- Cost price is 70% of marked price. So, if marked is M, cost is 0.7M.

- Profit : Discount = 2 : 1.

- Total revenue from 700 Y = Rs. 1,26,000. So, per article revenue = 1,26,000 / 700 = Rs. 180.

For Type X:

- Let’s call cost price = 8k, marked price = 15k.

- Let selling price be S.

- So, profit = S - 8k, discount = 15k - S.

- The key line: Profit % = 80% more than discount %

- Discount % = (15k - S)/15k × 100%

- Profit % = (S - 8k)/8k × 100%

- Now, Profit % = Discount % + (80% of Discount %) = 1.8 × Discount %

- So, (S - 8k)/8k = 1.8 × (15k - S)/15k

- Solve this and you’ll get S in terms of k:

- (S - 8k)/8k = 1.8 × (15k - S)/15k

- Cross-multiply:

(S - 8k) × 15k = 1.8 × 8k × (15k - S)

15kS - 120k² = 14.4k(15k - S)

15kS - 120k² = 216k² - 14.4kS

15kS + 14.4kS = 216k² + 120k²

29.4kS = 336k²

S = (336/29.4)k = 11.43k

- But remember, selling price per piece = Rs. 125.

- So, 11.43k = 125 ? k ˜ 10.93

- So, cost price per piece = 8k ˜ 87.43, profit per piece = 125 - 87.43 = Rs. 37.57

For Type Y:

- Selling price per piece = Rs. 180.

- Let’s set marked price = M, cost = 0.7M, S = 180.

- Profit = S - 0.7M

- Discount = M - S

- Profit : Discount = 2 : 1

- So, S - 0.7M = 2 × (M - S)

- S - 0.7M = 2M - 2S

- S + 2S = 2M + 0.7M

- 3S = 2.7M

- S = 0.9M

- But S = 180 ? 0.9M = 180 ? M = 200

- Cost = 0.7 × 200 = 140

- Profit per article = 180 - 140 = Rs. 40

The main question:

What % is profit per X over profit per Y?

- Profit per X ˜ Rs. 37.57

- Profit per Y = Rs. 40

So, % = (37.57 / 40) × 100 = 93.93%

Here’s what it means:

- None of the options you listed matches 93.93%.

- Option 3 (112.5%) is not correct ()

Summary of key points:

- X type profit per article ˜ Rs. 37.57, Y type profit per article = Rs. 40

- Profit on X is 93.93% of that on Y

- None of the answer options are correct, but it’s definitely NOT 112.5%

So the closest, most honest answer I can give:

And here’s the breakdown you asked for, with the math to show why.