Question

The l.c.m and h.c.f of two positive numbers are 175 and 5 respectively. if sum of the numbers is 60, what is the difference between them?

Answer 1

Here is the answer hope it helps

Answer 2

Answer:

The difference in the number is 10

Step-by-step explanation:

Given : The l.c.m and h.c.f of two positive numbers are 175 and 5 respectively. if sum of the numbers is 60.

To find : What is the difference between them?

Solution :

Let the numbers be x and y

HCF of the number = 5

LCM of the numbers= 175

We know,

$\text{Product of two numbers}=\text{HCF} \times \text{LCM}$

$x\times y=5\times 175$

$xy=875$ .......[1]

If sum of the numbers is 60

$x+y=60$  ..........[2]

Solving equation [1] and [2]

Substitute the value of y from [1] in [2]

$x+\frac{875}{x}=60$

$\frac{x^2+875}{x}=60$

$x^2+875=60x$

$x^2-60x+875=0$

$x^2-25x-35x+875=0$

$x(x-25)-35(x-25)=0$

$(x-35)(x-25)=0$

x=35 or x=25

Substitute in [2]

$x+y=60$

For x=35,

$35+y=60$

$y=25$

For x=25,

$25+y=60$

$y=35$

i.e, there are two values (35,25) or (25,35)

The difference in the numbers is 35-25= 10