Question

The sum of two numbers is 275 and their HCF is 25. If each of the two numbers lies between 100 and 160,then the sum of their reciprocals is-

Answer 1

$650$
8ihU oh yogi

Answer 2

Answer:

$Sum = \frac{11}{750}$

Step-by-step explanation:

Let the numbers be x and y

According as the question : x + y =275

We take GCD (Greatest Common Divisor)  for numbers )  and  HCF (highest common factor) for Algebraic expressions)

So, as we took are numbers as variables so taking given HCF as GCD

GIVEN :  GCD (x, y, 275) = 25

As GCD is greatest common divisor so it implies that x and y are also multiples of 25

Since x and  y both lies between 100 and 160, so the only value for x and y which is possible according to the given conditions are : 150 and 125.  (which are interchangeable)

$\text{Now, the sum of their reciprocals is = }\frac{1}{125} +\frac{1}{150}=\frac{11}{750}\\\\\text{So, the answer is }\frac{11}{750}$