Question

if the numerator of a fraction is the ncreased by 20% and the denominator is decreased by 5%,the value of the new fraction becomes 5/2.​

Answer 1

EXPLANATION.

• GIVEN

numerator of a fraction is increased by = 20%

denominator of a fraction is decreased by = 5%

the value of new fraction becomes = 5/2

To find original fraction,

Let the numerator be = x

Let the denominator be = y

Fraction = x / y

according to the question,

Numerator is increased by = 20%

$x + \frac{20}{100} x = \frac{120x}{100}$

Denominator is decreased by = 5%

$y - \frac{5}{100}y = \frac{95y}{100}$

Fraction become = 5/2

Therefore,

$\frac{ \frac{120x}{100} }{ \frac{95y}{100} } = \frac{5}{2}$

$\frac{120x}{100} \times \frac{100}{95y} = \frac{5}{2}$

$\frac{120x}{95y} = \frac{5}{2}$

$\frac{x}{y} = \frac{95 \times 5}{120 \times 2}$

$\frac{x}{y} = \frac{95}{48}$

Therefore,

Fraction become = 95/48

Answer 2

r/s = 95/48 .

Given that :-

1. The numerator of a fraction is the increased by 20% .
2. The denominator is decreased by 5%.
3. The value of the new fraction becomes 5/2.

To Find :-

• Original fraction.

Solution :-

Let,

• The numerator of the fraction be " r ".
• The denominator of the fraction be "s".

According to first Statement ,

$\tt \: r \: + \frac{20r}{100} = { \blue{\frac{120r}{100} }}$

According to second statement ,

$\tt \: s \: - \frac{5s}{100} = { \red{\frac{95s}{100} }}$

According to third statement ,

$\tt \: \green{\frac{ \frac{120r}{100} }{ \frac{95s}{100} } = \frac{5}{2}}$

$\tt \: \frac{120r}{ \cancel{100} } \times \frac{ \cancel{100}}{95s} = \frac{5}{2}$

$\tt \: \frac{120r}{95s} = \frac{5}{2}$

$\tt \: \frac{r}{s} = \frac{95}{120} \times \frac{5}{2}$

$\tt \frac{r}{s} = \frac{95 \times 5}{120 \times 2}$

$\tt \: \frac{r}{s} = \frac{ \cancel{475 }}{ { \cancel{240}}}$

$\tt \: \huge{ \red{\boxed{\tt{ \frac{r}{s} = \frac{95}{48} }}}}$

Hence,

• Original Fraction = 95/48.