Question

the numerator of a fraction is 4 less than the denominator . if 1 is subtracted from numerator and 3 is added to the denominator fraction becomes 1by5 .find the original fraction​

Answer 1

Question:-

The numerator of a fraction is 4 less than the denominator . if 1 is subtracted from numerator and 3 is added to the denominator fraction becomes 1/5 .find the original fraction.

Solution:-

Given,

• The numerator of fraction is 4less than the denominator.
• If 1 subtracted from numerator and 3 is added to denominator fraction becomes 1/5.

x + 4 = y

x = -4 + y .........( 1 )

Now,

$\frac{x \: - \: 1}{y \: + 3} \: = \frac{1}{5}$

Cross multiply

➦ 5( x - 1 ) = 1( y + 3 )

➦ 5x - 5 = y + 3

➦ 5x = y + 5 + 3

➦ 5x = y + 8 .........( 2 )

Put,

( 1 ) in ( 2 )

➦ 5 ( -4 + y ) = y + 8

➦ -20 + 5y = y + 8

➦ -20+ 5y - y = 8

➦ -20 + 4y = 8

➦ 4y = 8 + 20

➦ y = 28/4

$\boxed{ \: y \: = \: 7 \: }$

Now,

Substitute y in equation ( 1 ) to get the value of x:-

➦ x = -4 + y

➦ x = -4 + 7

$\boxed{ \: x \: = \: 3 \: }$

Then,

∴ The faction is 3/7.