Q.7
| Items | Cost (₹) | Profit % | Marked Price (₹) |
|---|---|---|---|
| P | 5,400 | — | 5,860 |
| Q | — | 25 | 10,000 |
Details of prices of two items P and Q are presented in the above table.
The ratio of cost of item P to cost of item Q is 3:4. Discount is calculated as
the difference between the marked price and the selling price. The profit
percentage is calculated as the ratio of the difference between selling price
and cost, to the cost.
(Profit % = (Selling price − Cost) / Cost × 100)
The discount on item Q, as a percentage of its marked price, is ______.
- (A) 25
- (B) 12.5
- (C) 10
- (D) 5
Two 6 cm × 1 cm sheets form a cylinder and a cube, with volumes compared for the correct ratio.
Cylinder Volume Calculation
Sheet M rolls short 1 cm edges together, making 6 cm the circumference and 1 cm the height.
Circumference: 2πr = 6, so r = 3/π cm.
Volume: Vc = πr²h = π(3/π)²(1) = 9/π cm³, despite ends closed since paper forms lateral surface.
Cube Volume Calculation
Sheet N cuts into equal squares for largest closed cube.
Total area = 6 cm² fits six 1 cm × 1 cm faces exactly, side a = 1 cm.
Volume: Vb = a³ = 1 cm³.
Ratio and Correct Answer
Ratio Vc / Vb = 9/π. Correct option (C).
Options Analysis
- (A) π/2: Reverse, smaller value mismatches 9/π ≈ 2.86
- (B) 3/π: Matches if height misinterpreted as circumference — incorrect rolling
- (C) 9/π: Matches exact calculation
- (D) 3π: Swapped dimensions, larger incorrect value
Comparison Table
| Option | Ratio Value | Approx. | Matches? |
|---|---|---|---|
| (A) | π/2 | 1.57 | No |
| (B) | 3/π | 0.95 | No |
| (C) | 9/π | 2.86 | Yes |
| (D) | 3π | 9.42 | No |
