The Difference of Two Natural Numbers is 5 and the Difference of Their Reciprocals is 5/14. Find the Numbers. - Mathematics

Advertisements
Advertisements

The difference of two natural numbers is 5 and the difference of their reciprocals is 5/14. Find the numbers.

Advertisements

Solution

Let a and b be two natural number such that, a>b

Given,

`a−b=5 ...(1)`

`and 1/b−1/a=5/14`

`⇒(a−b)/(ab)=5/14`

`⇒5/(ab)=5/14`

`⇒ab=14 ...(2)`

Putting the value of a from equation (1) in equation (2), we get

(5+b)b=14

⇒5b+b2=14

⇒b2+5b−14=0

⇒b2+7b−2b−14=0

⇒b(b+7)−2(b+7)=0

⇒(b−2)(b+7)=0

⇒b=2 or b=−7

Since, b is natural number, neglecting the value, b = −7,we get
b=2⇒a=b+5=2+5=7

So, the required natural numbers are 7 and 2.

  Is there an error in this question or solution?
2013-2014 (March) Delhi Set 3

RELATED QUESTIONS

A three digit number is equal to 17 times the sum of its digits. If 198 is added to the number, the digits are interchanged. The addition of first and third digit is 1 less than middle digit. Find the number.


If the point (3, 2) lies on the graph of the equation 5x + ay = 19, then find a.


The difference of two natural numbers is 3 and the difference of their reciprocals is 3/28 . Find the numbers


Solve the following pair of linear equations by the substitution method

3x – y = 3 

9x – 3y = 9


Solve the following simultaneous equations

`1/(3x)-1/(4y)+1=0`;

`1/(5x)+1/(2y)=4/15`


Solve the following systems of equations:

`15/u + 2/v = 17`


Solve the following systems of equations:

`2/x + 3/y = 9/(xy)`

`4/x + 9/y = 21/(xy), where x != 0, y != 0`


Solve the following systems of equations:

x − y + z = 4
x + y + z = 2
2x + y − 3z = 0


5 books and 7 pens together cost Rs 79 whereas 7 books and 5 pens together cost Rs 77. Find the total cost of 1 book and 2 pens.


On selling a T.V. at 5%gain and a fridge at 10% gain, a shopkeeper gains Rs 2000. But if he sells the T.V. at 10% gain and the fridge at 5% loss. He gains Rs 1500 on the transaction. Find the actual prices of T.V. and fridge.


Solve the following simultaneous equations by Cramer's method. 

`x+y=7,2x-3y=9` 

 


Solve the following system of equations by eliminating ‘y’ (by substitution) :

2x + y = 0

17x – 11y – 8 = 0


Solve the following set of simultaneous equation.

x + y = 4 ; 2x - 5y = 1


Solve the following set of simultaneous equation. 

2x + y = 5; 3x - y = 5


Solve the following set of simultaneous equation.

3x - 5y = 16; x - 3y = 8


Solve the following set of simultaneous equation.

2y - x = 0; 10x + 15y = 105


Solve the following set of simultaneous equation.

2x + 3y + 4 = 0; x - 5y = 11


Solve the following set of simultaneous equation.

2x - 7y = 7; 3x + y = 22


The sum of ages of Priyanka and Deepika is 34 years. Priyanka is elder to Deepika by 6 years. Then find their today's ages.


The price of 3 chairs and 2 tables is 4500 rupees and price of 5 chairs and 3 tables is 7000 rupees, then find the price of 2 chairs and 2 tables.


Divide a rope of length 560 cm into 2 parts such that twice the length of the smaller part is equal to `1/3` of the larger part. Then find the length of the larger part.


The solution of the equation x − y = 10 and x + y = 70 is ______


For the equation 4x + 5y = 20 find y when x = 0


If x + 2y = 5 and 2x + y = 7, then find the value of x + y


In the equation 2x – y = 2 if x = 3, then find y = ?


For the equation a + 2b = 7, find a when b = 4


Using variables a and b write any two equations whose solution is (0, 2).


Ajay is younger than Vijay by 3 years. The sum of their ages is 25 years, what is the age of Ajay


For the equation 3x − 2𝑦𝑦 = 17, find the value of x when y = −1 and find the value of y when x = 3


For an A.P., t17 = 54 and t9 = 30 find the first term(a) and common difference(d)


A train covered a certain distance at a uniform speed. If the train would have been 6 km/h faster, it would have taken 4 hours less than the scheduled time. And, if the train was slower by 6 km/h it would have taken 6 hours more than the scheduled time. Find the length of the journey.


If (x + 1) is a factor of 2x3 + ax2 + 2bx + 1, then find the values of a and b given that 2a – 3b = 4.


Two numbers are in the ratio 5 : 6. If 8 is subtracted from the numbers, the ratio becomes 4 : 5. Find the numbers.


To draw a graph of 4x + 5y = 19, find y when x = 1.


Solve x + 2y = 10 and 2x + y = 14 by substitution method and hence find the value of m for which y = mx + 8.


Share
Notifications



      Forgot password?
Use app×