Question

the numerator & denominator
of fraction increased & decreased
by 12% & 10% respectively
& the fraction becomes 224/270.
what is the original fraction?​

Answer 1

Answer:

dont know

Step-by-step explanation:

Answer 2

The original fraction is 2/3

Step-by-step explanation:

Given:

the numerator is increased by 12% & denominator is decreased by 10%

the fraction then equals 224/270

To find:

original fraction

Solution:

Let's say the numerator is x and the denominator is y

Thus, the fraction will be x/y

The numerator is increased by 12% and the denominator is decreased by 10% to obtain the fraction 224/270

According to the condition given,

Assuming the numerator x is increased by 12% and denominator y is decreased by 10%

x+ 12 % of x =   224

y- 10% of y        270

∴ $\frac{x+\frac{3x}{25} }{y-\frac{y}{10} } = \frac{224}{270}$

Cross multiplying the terms in numerator and denominator

∴  $\frac{\frac{25x+3x}{25} }{\frac{10y-y}{10}}=\frac{224}{270}$

∴  $\frac{\frac{28x}{25} }{\frac{9y}{10} } =\frac{224}{270}$

Simplifying and bringing like terms together

∴ $\frac{x}{y} =\frac{224}{270} \ X \frac{9}{10} \ X \frac{25}{28}$

∴ $\frac{x}{y} =\frac{2016}{2700} \ X \frac{25}{28}$

∴ $\frac{x}{y} =\frac{50400}{75600}$

$\frac{x}{y} =\frac{504}{756}$

Simplifying it further we get

$\frac{x}{y} =\frac{6}{9}$

∴ $\frac{x}{y} =\frac{2}{3}$

∴ x/y = 2/3

Thus, the original fraction is 2/3

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