Question

If the numerator of a fraction is multiplied by 2 and its denominator is increased by 2, it becomes 6/7. If instead we multiply the denominator by 2 and increase the numerator by 2 it reduces to 1/2. What is the fraction?

Answer 1

The numerator is 3 so when we multiply it with 2 then we get 6.If the denominator is 5 and if we add 2 for it it will be 7.then it is 6/7.the numerator 3 is increased to 2=5 then 5 the denominator is multiplied by 2 =10.then fraction is 5/10.it's simplest form is 1/2.

Answer 2

Hi there!
Here's the answer:

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Let the original fraction be (x/y)

Given,
If the numerator of a fraction is multiplied by 2 and its denominator is increased by 2, (x/y) becomes 6/7.

(2x)/(y+2) = (6/7)
=> 7(2x) = 6(y+2)
=> 14x - 6y = 12
=> 7x - 3y = 6
……………………………eq(1)

&

If the denominator is multiplied by 2 and increase the numerator by 2,(x/y) reduces to 1/2

(x+2)/(2y) = (1/2)
=> 2(x+2) = (2y)
=> 2x - 2y = -4
=> x - y = -2
……………………………eq(2)

Solve eq(1) & eq(2):

x = 3 & y = 5

•°• Original fraction (x/y) = (3/5)

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Verification:

Fraction = (3/5)
(2×3)/(5+2)= 6/7
(3+2)/(2×5) = 5/10 = 1/2
•°• Given Data matched

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:)

Hope it helps