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If \(A=\dfrac{3}{7}\times\dfrac{9}{28}\div\dfrac{81}{343}\) and \(B=\dfrac{4}{5}\div\dfrac{16}{25}+\dfrac{3}{7}\times\dfrac{28}{27}\), then what is the value of B/A?
1. 1301/661
2. 1211/371
3. 1291/441
4. 1281/441

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Correct Answer - Option 4 : 1281/441

Given:

A = (3/7) × (9/28) ÷ (81/343)

B = (4/5) ÷ (16/25) + (3/7) × (28/27)

Calculation:

According to the question,

A = (3/7) × (9/28) ÷ (81/343)

⇒ (3/7) × (9/28) × (343/81)

⇒ (3/7) × (1/4) × (49/9)

⇒ (1/4) × (7/3)

⇒ 7/12

Now, B = (4/5) ÷ (16/25) + (3/7) × (28/27)

⇒ (4/5) × (25/16) + 4/9

⇒ (5/4) + (4/9)

⇒ 61/36

Now, 

B/A = (61/36)/(7/12)

⇒ (61/36) × (12/7)

⇒ (61/3) × (1/7)

⇒ 61/21

⇒ (61 × 21)/(21 × 21)

⇒ 1281/441

∴ The value of B/A is 1281/441.

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