Math, asked by diyaa3661, 11 months ago

if the numerator of a fraction is increase by 200% and the denominator by 150% the resultant fraction is 9/35. what is the original fraction?

vijaymano0123: hi diyaa

vijaymano0123: I am in Tn. Where r u ya

Answers

Answered by TooFree

Define the fraction:

$\text{Fraction} = \dfrac{x}{y}$

Numerator increased by 200% and denominator increased by 150%:

$\dfrac{x + 2x}{y+ 1.5y} = \dfrac{9}{35}$

$\dfrac{3x}{2.5y} = \dfrac{9}{35}$

Find x

3x = 9

x = 9 ÷ 3

x = 3

Find y:

2.5y = 35

y = 35 ÷ 2.5

y = 14

ANSWER:

$\text{Original Fraction} = \dfrac{3}{14}$

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ALTERNATIVE METHOD:

Define the fraction:

$\text{Fraction} = \dfrac{x}{y}$

Numerator increased by 200% and denominator increased by 150%:

$\dfrac{x + 2x}{y+ 1.5y} = \dfrac{9}{35}$

$\dfrac{3x}{2.5y} = \dfrac{9}{35}$

Find the fraction:

$\dfrac{3x}{2.5y} = \dfrac{9}{35}$

$\dfrac{x}{y} \times\dfrac{3}{2.5} = \dfrac{9}{35}$

$\dfrac{x}{y} = \dfrac{9}{35} \div \dfrac{3}{2.5}$

$\dfrac{x}{y} = \dfrac{9}{35} \times \dfrac{2.5}{3}$

$\dfrac{x}{y} = \dfrac{3}{14}$

ANSWER:

$\text{Original Fraction} = \dfrac{3}{14}$

TooFree: I can equate it because they are increased in proportional to each other. Okay, I will edit it to show you why it would mean the same. Give me a while.

jyothsna98: kk

jyothsna98: say fast

TooFree: Here. edited

jyothsna98: can i know ur real name

TooFree: I like to be addressed as "toofree"

jyothsna98: why

santosh8872: ur correct

jyothsna98: can i know who is correct

sheshank9866: hii

Answered by jyothsna98

x*200/100=2x
y*150/100=1.5y
2x/1.5y=9/35
2x*35=1.5y*9
70x=13.5y
x/y=13.5/70
x/y= 135/700
hence the original fraction is 135/700

TooFree: The question says the numerator is increased by 200%, not increased to 200%. So your x should be (x + 2x) and not just 2x.

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