if x/y = 4/5, then the value of 5/8 + (y - x)/(y + x) is1. \(\frac{4

1.	if x/y = 4/5, then the value of 5/8 + (y - x)/(y + x) is1. \(\frac{49}{72}\)2. \(\frac{53}{72}\)3. \(\frac{23}{24}\)4. None of the above
Answer» Correct Answer - Option 2 : \(\frac{53}{72}\) Given: x/y = 4/5 Calculations: (y - x) divide each term with y = [(y/y) - (x/y)] ⇒ (1 - x/y) (y + x) divide each term with y = [(y/y) + (x/y)] ⇒ (1 + x/y) (5/8) + (y - x)/(y + x) = 5/8[(1 - x/y) ÷ (1 + x/y)] ⇒ (5/8) + [(1 - 4/5) ÷ (1 + 4/5)] = (5/8) + {[(5 - 4)/5] ÷ [(5 + 4)/5]} ⇒ (5/8) + {[(5 - 4)/5] ÷ [(5 + 4)/5]} = (5/8) + [(1/5) ÷ (9/5)] ⇒ 5/8 + 1/9 = (5× 9 + 1 × 8)/(8 × 9) ⇒ (45 + 8)/72 = 53/72 ∴ The required value is 53/72

if x/y = 4/5, then the value of 5/8 + (y - x)/(y + x) is1. \(\frac{49}{72}\)2. \(\frac{53}{72}\)3. \(\frac{23}{24}\)4. None of the above

Answer» Correct Answer - Option 2 : \(\frac{53}{72}\)

Given:

x/y = 4/5

Calculations:

(y - x) divide each term with y = [(y/y) - (x/y)]

⇒ (1 - x/y)

(y + x) divide each term with y = [(y/y) + (x/y)]

⇒ (1 + x/y)

(5/8) + (y - x)/(y + x) = 5/8[(1 - x/y) ÷ (1 + x/y)]

⇒ (5/8) + [(1 - 4/5) ÷ (1 + 4/5)] = (5/8) + {[(5 - 4)/5] ÷ [(5 + 4)/5]}

⇒ (5/8) + {[(5 - 4)/5] ÷ [(5 + 4)/5]} = (5/8) + [(1/5) ÷ (9/5)]

⇒ 5/8 + 1/9 = (5× 9 + 1 × 8)/(8 × 9)

⇒ (45 + 8)/72 = 53/72

∴ The required value is 53/72