English

The Sum of Two Natural Number is 28 and Their Product is 192. Find the Numbers. - Mathematics

Advertisements
Advertisements

Question

The sum of two natural number is 28 and their product is 192. Find the numbers. 

Advertisements

Solution

Let the required number be x and (28-x).
According to the given condition, 

`x(28)-x=192` 

⇒`28x-x^2=192` 

⇒`x^2-28x+192=0` 

⇒`x^2-16x-12x+192=0` 

⇒`x(x-16)-12(x-16)=0` 

⇒`(x-12)(x-16)=0` 

⇒`x-12=0  or x-16=0` 

⇒`x=12 or  x=16` 

when` x=12` 

`28-x=28-12=16` 

when `x=16`  

28-x=28-16=12` 

Hence, the required numbers are 12 and 16. 

shaalaa.com
  Is there an error in this question or solution?
Chapter 10: Quadratic Equations - Exercises 5

APPEARS IN

R.S. Aggarwal Mathematics [English] Class 10
Chapter 10 Quadratic Equations
Exercises 5 | Q 3

RELATED QUESTIONS

Solve the following quadratic equations by factorization:

a2x2 - 3abx + 2b2 = 0


Solve the following quadratic equations by factorization:

`(x-1)/(x-2)+(x-3)/(x-4)=3 1/3`, x ≠ 2, 4


The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.


A fast train takes one hour less than a slow train for a journey of 200 km. If the speed of the slow train is 10 km/hr less than that of the fast train, find the speed of the two trains.


Out of a group of swans, 7/2 times the square root of the total number are playing on the share of a pond. The two remaining ones are swinging in water. Find the total number of swans.


The sum of two natural numbers is 15 and the sum of their reciprocals is `3/10`. Find the numbers.


One of the roots of equation 5m2 + 2m + k = 0 is `(-7)/5` Complete the following activity to find the value of 'k'.


Solve the following quadratic equation by factorisation.

 x2 – 15x + 54 = 0


Solve the following quadratic equation by factorisation.

2m (m − 24) = 50


The distance between Akola and Bhusawal is 168 km. An express train takes 1 hour less than a passenger train to cover the distance. Find the average speed of each train if the average speed of the express train is more by 14 km/hr than the speed of the passenger train. 


If 1 is a root of the quadratic equation \[3 x^2 + ax - 2 = 0\] and the quadratic equation \[a( x^2 + 6x) - b = 0\] has equal roots, find the value of b.


If one of the equation x2 + ax + 3 = 0 is 1, then its other root is


The area of right-angled triangle is 600cm2. If the base of the triangle exceeds the altitude by 10cm, find the dimensions of the triangle.


Solve the following equation by factorization

`(2)/(3)x^2 - (1)/(3)x` = 1


Solve the following equation by factorization

x2– 4x – 12 = 0,when x∈N


Solve the following equation by factorization

`x/(x - 1) + (x - 1)/x = 2(1)/(2)`


Solve the following equation by factorization

`(1)/(2a + b + 2x) = (1)/(2a) + (1)/b + (1)/(2x)`


Five times a certain whole number is equal to three less than twice the square of the number. Find the number.


A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.


Is 0.2 a root of the equation x2 – 0.4 = 0? Justify


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×