Given:
A. A shopkeeper incurs a loss of 20% by selling an item for ₹560, Cost Price = ₹750.
B. 10% of 20% of 25% of 200 = 1.
C. 25% of x = 30% of y, y = 5000, x = ?.
D. A person gains 6.25% by selling an item for ₹29.75, Cost Price = ₹26.
Formula used:
- Loss% = (Loss ÷ Cost Price) × 100.
- Percentage calculation: Result = (x% of y).
- 25% of x = 30% of y ⇒ x = (30 × y) ÷ 25.
- Gain% = (Gain ÷ Cost Price) × 100.
Calculations:
A. Loss of 20%:
Loss% = (Loss ÷ Cost Price) × 100.
Loss = Cost Price - Selling Price.
⇒ 20% = ((CP - 560) ÷ CP) × 100.
⇒ 20 = ((CP - 560) ÷ CP) × 100.
⇒ CP = 560 ÷ (1 - (20 ÷ 100)) = 560 ÷ 0.8 = ₹700 (not ₹750).
B. 10% of 20% of 25% of 200:
⇒ (10 ÷ 100) × (20 ÷ 100) × (25 ÷ 100) × 200.
⇒ 0.1 × 0.2 × 0.25 × 200 = 1.
⇒ Correct.
C. 25% of x = 30% of y:
⇒ 25 ÷ 100 × x = 30 ÷ 100 × y.
⇒ x = (30 × y) ÷ 25 = (30 × 5000) ÷ 25 = ₹6000.
⇒ Correct.
D. Gain of 6.25%:
Gain% = (Selling Price - Cost Price) ÷ Cost Price × 100.
⇒ 6.25% = (29.75 - CP) ÷ CP × 100.
⇒ 6.25 = (29.75 - CP) ÷ CP × 100.
⇒ CP = 29.75 ÷ (1 + (6.25 ÷ 100)) = 29.75 ÷ 1.0625 = ₹28 (not ₹26).
Final Answer:
The correct statements are B and C only.