Question

in a given fraction if the num is multiplied by 2 and the deno is reduced by 5 we get 6/5 but if the num of the given fraction is increased by 8 and tge deno is doubled we get ⅖ find the fraction​

Answer 1

Step-by-step explanation:

⇒ 2a/(b - 5) = 6/5

⇒ 10a = 6b - 30

⇒ 5a = 3b - 15

⇒ 5a - 3b = - 15 .....(i)

Also given, the numerator is increased by 8 and the denominator is doubled, and thus we get 2/5.

⇒ (a + 8)/2b = 2/5

⇒ 5a + 40 = 4b

⇒ 5a - 4b = - 40 .....(ii)

Thus, we get two equations with variables a and b as follows :

5a - 3b = - 15 .....(i)

5a - 4b = - 40 .....(ii)

On subtraction, we get

(5a - 3b) - (5a - 4b) = - 15 - (- 40)

⇒ 5a - 3b - 5a + 4b = - 15 + 40

⇒ b = 25

Now, putting b = 25 in (i), we get

5a - (3 × 25) = - 15

⇒ 5a - 75 = - 15

⇒ 5a = - 15 + 75

⇒ 5a = 60

⇒ a = 12

So, the required fraction is = 12/25.

CONFIRMATION :

The fraction is = 12/25

For the first condition,

(12 × 2)/(25 - 5)

= 24/20

= (4 × 6)/(4 × 5)

= 6/5

For the second condition,

(12 + 8)/(25 × 2)

= 20/50

= (10 × 2)/(10 × 5)

= 2/5

Hence, confirmed.