Read the given statements carefully and state 'T' for true and 'F' for false.
(i) If the ratio of three numbers is 3 : 4 : 5 and sum of their squares is 1250, then the sum of numbers is 60.
(ii) Decrease % = `(("Decreased value")/("New value") xx 100)%`
(iii) If an article is sold for Rs p after giving a discount of q %, then its marked price is Rs `(100p)/(100-q)`
(iv) If 44% of a number is 275, then 64 % of the same number is 400.

Options

A. `{:(i,ii,iii,iv),(F,F,T,T):}`
B. `{:(i,ii,iii,iv),(T,F,T,T):}`
C. `{:(i,ii,iii,iv),(T,F,F,T):}`
D. `{:(i,ii,iii,iv),(F,T,F,T):}`

Answer

Let's solve the statements step by step.

### Statement (i)
**Statement:** If the ratio of three numbers is 3 : 4 : 5 and the sum of their squares is 1250, then the sum of the numbers is 60.

**Solution:**
1. Let the three numbers be \(3x\), \(4x\), and \(5x\).
2. The sum of their squares is:
\[ (3x)^2 + (4x)^2 + (5x)^2 = 9x^2 + 16x^2 + 25x^2 = 50x^2 \]
3. Set this equal to 1250:
\[ 50x^2 = 1250 \]
4. Divide both sides by 50:
\[ x^2 = \frac{1250}{50} = 25 \]
5. Take the square root of both sides:
\[ x = 5 \]
6. Now, calculate the three numbers:
- \(3x = 3 \times 5 = 15\)
- \(4x = 4 \times 5 = 20\)
- \(5x = 5 \times 5 = 25\)
7. The sum of the numbers is:
\[ 15 + 20 + 25 = 60 \]

**Conclusion:** The statement is **True (T)**.

### Statement (ii)
**Statement:** Decrease % = \(\frac{\text{Decreased value}}{\text{New value}} \times 100\)%

**Solution:**
1. The formula for decrease percentage is actually:
\[ \text{Decrease %} = \frac{\text{Decreased value}}{\text{Original value}} \times 100 \]
2. This means the statement is incorrect because it uses "New value" instead of "Original value".

**Conclusion:** The statement is **False (F)**.

### Statement (iii)
**Statement:** If an article is sold for Rs \(p\) after giving a discount of \(q\%\), then its marked price is Rs \(\frac{100p}{100-q}\).

**Solution:**
1. Let the marked price be \(MP\).
2. The selling price \(SP\) after discount is given by:
\[ SP = MP - \text{Discount} \]
3. The discount can be expressed as:
\[ \text{Discount} = \frac{q}{100} \times MP \]
4. Therefore, we can write:
\[ p = MP - \frac{q}{100} \times MP \]
5. Rearranging gives:
\[ p = MP \left(1 - \frac{q}{100}\right) = MP \left(\frac{100 - q}{100}\right) \]
6. Solving for \(MP\):
\[ MP = \frac{100p}{100 - q} \]

**Conclusion:** The statement is **True (T)**.

### Statement (iv)
**Statement:** If 44% of a number is 275, then 64% of the same number is 400.

**Solution:**
1. Let the number be \(X\).
2. According to the statement:
\[ 0.44X = 275 \]
3. Solving for \(X\):
\[ X = \frac{275}{0.44} = 625 \]
4. Now, calculate 64% of \(X\):
\[ 0.64 \times 625 = 400 \]

**Conclusion:** The statement is **True (T)**.

### Final Answers
- (i) T
- (ii) F
- (iii) T
- (iv) T

The final answer is **TFTT**.