Question

The numerator of a fraction is increased
by 20%. and the denominator is
decreased by 20%.The value of fraction becomes 4/5.The original fraction is.​

Answer 1

Answer:

The original fraction is 8/15.

Step by step explanation:

Let the numerator of the original fraction be x

and denomination be y.

so the original fraction will be x / y

Now,

the numerator is increased by 20%

so, new numerator = x + 20% of x

= 1.2 x

the denominator is decreased by 20%

so, new denominator = y - 20% of y

= 0.8 y

So, the new fraction will be 1.2 x / 0.8 y

= 1.2/0.8 x / y

= 3/2 x / y

= 3/2 x Original fraction

But according to the question;

Value of New fraction = 4/5

so, 3/2 x Original fraction = 4/5

so, Original fraction = 4/5 x 2/3

so, Original fraction = 8/15

Hence , the original fraction is 8/15.

Answer 2

Answer:

★ Fraction = 8/15 ★

Step-by-step explanation:

Given:

• Numerator of fraction is increased by 20%
• Denominator is decreased by 20%
• Value of Fraction becomes 4/5

To Find:

• What is the original fraction?

Solution: Let the numerator be n and denominator be d

∴ Fraction will be numerator/denominator

†After increasing numerator by 20% †

$\small\implies{\sf }$ n + 20% of n

$\small\implies{\sf }$ n + 20n /100 [ Take LCM ]

$\small\implies{\sf }$ 100n + 20n/100

$\small\implies{\sf }$ 120n/100

$\small\implies{\sf }$ Numerator = 12n/10 .......(1)

†After decreasing denominator by 20%†

$\small\implies{\sf }$ d – 20% of d

$\small\implies{\sf }$ d – 20d/100 [ Take LCM ]

$\small\implies{\sf }$ 100d – 20d/100

$\small\implies{\sf }$ 80d/100

$\small\implies{\sf }$ Denominator = 8d/10 .......(2)

A/q

$\small\implies{\sf }$ n/d = 4/5

• Putting the values of n and d from equations 1 and 2 •

$\small\implies{\sf }$ 12n/10/8d/10 = 4/5

$\small\implies{\sf }$ 12n/10 x 10/8d = 4/5

$\small\implies{\sf }$ 120n/80d = 4/5

$\small\implies{\sf }$ n/d = 4/5 x 80/120

$\small\implies{\sf }$ n/d = 320/600

$\small\implies{\sf }$ n/d = 32/60

$\small\implies{\sf }$ n/d = 16/30

$\small\implies{\sf }$ n/d = 8/15

Hence, The original fraction is n/d = 8/15