Question

A fraction becomes 8/11 if 3 is added to both numerator and denominator ,also if 3 is subtracted from the numerator and denominator it becomes 2/5. Find the fraction?​

Answer 1

Given data : A fraction becomes 8/11 if 3 is added to both numerator and denominator ,also if 3 is subtracted from the numerator and denominator it becomes 2/5.

Now to find fraction?

Solution : Let, numerator be x and denominator be y.

Now according to given :

⟹ numerator/denominator = x/y

After adding 3 both numerator and denominator.

⟹ {x + 3}/{y + 3} = 8/11

⟹ 11 * {x + 3} = 8 * {y + 3}

⟹ 11x + 33 = 8y + 24

⟹ 11x - 8y = 24 - 33

⟹ 11x - 8y = - 9 ____( 1 )

Now, after subtracting 3 from both numerator and denominator.

⟹ {x - 3}/{y - 3} = 2/5

⟹ 5 * {x - 3} = 2 * {y - 3}

⟹ 5x - 15 = 2y - 6

⟹ 5x - 2y = - 6 + 15

⟹ 5x - 2y = 9 ____( 2 )

Now multiply eq. ( 1 ) by 5 and eq. ( 2 ) by 11

then equations becomes respectively.

⟹ 55x - 40y = - 45 ____( 3 )

⟹ 55x - 22y = 99 ____( 4 )

Now, subtract eq. ( 4 ) from eq. ( 3 )

55x - 40y = - 45

- ( 55x - 22y = 99 )

___________________

- 18y = - 144

18y = 144

y = 144/18

y = 8

Put value of y in eq. ( 1 )

⟹ 11x - 8y = - 9

⟹ 11x - 8 * 8 = - 9

⟹ 11x - 64 = - 9

⟹ 11x = - 9 + 64

⟹ 11x = 55

⟹ x = 55/11

⟹ x = 5

so, numerator/denominator = x/y = 5/8

Answer : Hence, fraction is 5/8.

Answer 2

Answer:

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