Question

In given fraction, if the numerator is multiplied by 2 and denominator is reduced by 5,we get 6/5. But if the numerator of given fraction is increased by 8 and denominator is double, we get 2/5. Find the fraction..


Please solve this question........

Answer 1

The answer is given below :

SOLUTION :

Let us consider the fraction as a/b,
where both a and b are real numbers.

By the given condition, the numerator is multiplied by 2 and the denominator is reduced by 5, and thus we get 6/5.

⇒ 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.

Thank you for your question.

Answer 2

Heya !!

Here's your answer..⤵
_________________

Let numerator = x
Denominator = y

so, we get fraction = numerator/denominator
= x/y

⏩Given that if the numerator is multiplied by 2 and denominator is reduced by 5,we get 6/5.

Numerator multiply by 2 = 2x
Denominator is reduced by 5 = y - 5

so,
2x/( y-5 ) = 6/5

5( 2x ) = 6( y-5 )

10x = 6y - 30

10x - 6y + 30 = 0

Taking 2 as a common ..,

5x - 3y +15 = 0

5x - 3y = -15 ---(1)

⏩Now,if the numerator of given fraction is increased by 8 and denominator is double, we get 2/5.

Numerator increase by 8 = x+8
Denominator is doubled = 2y

fraction will be = 2/5

(x+8)/2y = 2/5

5( x+8 ) = 2(2y)

5x + 40 = 4y

5x - 4y = -40 ---(2)


▶ Subtract eq.(1) from eq.(2)..

+5x - 4y = -40
-5x +3y = +15
----------------------
-y = -25

y = 25

put value of (y) in eq.(1)

5x - 3y = -15

5x - 3(25) = -15

5x -75 = -15

5x = -15 + 75

5x = 60

x = 12

put value of (x) and (y) in fraction..

Fraction = x/y

= 12/25

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Hope it helps..
Thanks ^^