CAT 1991 Question 23

Question 23

The sum of two integers is 10 and the sum of their reciprocals is 5/12. Then the larger of these integers is

Solution

let's say integers are x and y
so x+y = 10 => y = 10 - x
and $$\frac{1}{x} + \frac{1}{y} = \frac{5}{12}$$
$$\frac{1}{x} + \frac{1}{10-x} = \frac{5}{12}$$

=> (10 - x + x)*12 = 5*x(10-x)

=> $$120 = 50x - 5x^2$$

=> $$24 = 10x - x^2$$

=> x = 4, 6

=> y = 6 or 4

The bigger of the two numbers is 6.



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