Global Statistics

All countries
94,951,943
Confirmed
Updated on January 17, 2021 3:06 am
All countries
67,554,399
Recovered
Updated on January 17, 2021 3:06 am
All countries
2,030,924
Deaths
Updated on January 17, 2021 3:06 am

Global Statistics

All countries
94,951,943
Confirmed
Updated on January 17, 2021 3:06 am
All countries
67,554,399
Recovered
Updated on January 17, 2021 3:06 am
All countries
2,030,924
Deaths
Updated on January 17, 2021 3:06 am

The Difference between the Numerator and the Denominator of a Fraction is 5. If 5 is Added to its Denominator, the Fraction is Decreased by 5/4. Find the Value of the Fraction?

What are you looking for? Let’s dig in quickly

Explanation

  • The difference between the numerator and the denominator of a fraction is 5.
  • If 5 is added to its denominator, the fraction is decreased by 5/4.
  • The value of the fraction can be figure out in this way.

Let suppose y shows numerator and z shows denominator in a fraction.

The difference between y (numerator) and z (denominator) is 5.

y – z = 5 ________ (i)

The fraction (y/z) decreased by 5/4 when 5 is added to z (denominator).

y/(z +5) = y/z – 5/4 ________ (ii)

By solving both equations simultaneously, we can easily find out the fraction (y/z = 9/4).

To Find

Fraction = ?

Solution

Let suppose

Let suppose y shows numerator and z shows denominator in a fraction.

According to first given condition

y – z = 5 ________ (i)

y = 5 + z ________ (A)

According to second given condition

y/(z +5) = y/z – 5/4 ________ (ii)

y/(z + 5) = (4y – 5z)/4z

4yz = (4y – 5z)(z + 5)

4yz = 4yz + 20y – 5z2 – 25z

5z2 + 25z – 20y = 0

z2 + 5z – 4y = 0 ________ (B)

Put y = z + 5 in equation (B)

z2 + 5z – 4(z + 5) = 0

z2 + 5z – 4z – 20 = 0

z(z + 5) -4(z + 5) = 0

(z + 5)(z – 4) = 0

z + 5 = 0             &                z – 4 = 0

z = -5 (not possible)              &                z = 4 (possible)

Put z = 4 in equation (A)

y = 4 + 5

y = 9

Fraction = 9/4 answer

Conclusion

The difference between the numerator and the denominator of a fraction is 5. If 5 is added to its denominator, the fraction is decreased by 5/4. The fraction is 9/4.

LEAVE A REPLY

Please enter your comment!
Please enter your name here

Hot Topics

An industrial loom weaves 0.128 m of cloth every second. Approximately, how many seconds will take for the loom to weave 25 m of...

An industrial loom weaves 0.128 m of cloth every second. The time required for the loom to weave 25 m of cloth can be figure...

On a Scale of Map 0.6 cm Represents 6.6 km. If the Distance Between the Points on the Map is 80.5 cm, the Actual...

On a scale of map 0.6 cm represents 6.6 km. If the distance between the points on the map is 80.5 cm, the actual distance...

If 11.25m of a Uniform Iron Rod Weighs 42.75 kg What will be the Weight of 6m of the Same Rod?

If 11.25m of a uniform iron rod weighs 42.75 kg. The weight of 6m of the same rod can be figure out in this way. Explanation Solution Explanation Two...

Related Articles

An industrial loom weaves 0.128 m of cloth every second. Approximately, how many seconds will take for the loom to weave 25 m of...

An industrial loom weaves 0.128 m of cloth every second. The time required for the loom to weave 25 m of cloth can be figure...

On a Scale of Map 0.6 cm Represents 6.6 km. If the Distance Between the Points on the Map is 80.5 cm, the Actual...

On a scale of map 0.6 cm represents 6.6 km. If the distance between the points on the map is 80.5 cm, the actual distance...

If 11.25m of a Uniform Iron Rod Weighs 42.75 kg What will be the Weight of 6m of the Same Rod?

If 11.25m of a uniform iron rod weighs 42.75 kg. The weight of 6m of the same rod can be figure out in this way. Explanation Solution Explanation Two...
error: Content is protected !!