Question

If the numerator of a fraction is multiplied by 2 and the denominator is reduced by 5 the fraction becomes 6/5. And, if the denominator is doubled and the numerator is increased by 8, the fraction becomes 2/5. Find the fraction.

Class 10th

Content Quality Solution needed.

No Spams please otherwise will be reported or blocked account.

Answer 1

Heya !!!

Let the numerator and denominator of fraction be X and Y.

Fraction = Numerator/Denominator = X/Y.

According to question,

X × 2 / Y - 5 = 6/5

2X/Y-5 = 6/5

5 × 2X = 6(Y-5)

10X = 6Y - 30

10X - 6Y = -30------------(1)

And,

X + 8/2Y = 2/5

5(X+8) = 2Y × 2

5X + 40 = 4Y

5X - 4Y = -40-----------(2)

From equation (1) we get,

10X - 6Y = -30

10X = -30 + 6Y

X = -30+6Y/10---------(3)

Putting the value of X in equation (2)

5X - 4Y = -40

5 × (-30+6Y/10) - 4Y = -40

-30+6Y/2 - 4Y = -40

-30 + 6Y - 8Y/2 = -40

-2Y - 30 = -40 × 2

-2Y - 30 = -80

-2Y = -80+ 30

-2Y = -50

Y = -50/-2 => 25

Putting the value of Y in equation (3)

X = -30 + 6Y/10 => -30 + 6 × 25/10

X = -30 + 150/10 => 120/10 =12

Therefore,

Numerator of fraction = X = 12

And,

Denominator of fraction = Y = 25

Fraction = Numerator/Denominator = 12/25

HOPE IT WILL HELP YOU...... :-)