Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

If a, b, c are in GP and x,y are the arithmetic means between a,b and b,c respectively, then a/x + c/y is equal to

(1) 0

(2) 1

(3) 2

(4) ½

Solution:

Since a, b, c are in GP

b2 = ac

Since x is the arithmetic mean between a and b

x = (a+b)/2

Also y = (b+c)/2

a/x + c/y = 2a/(a+b) + 2c/(b+c)

= [2a(b+c) + 2c(a+b)]/(a+b)(b+c)

= (2ab + 2ac+ 2ac + 2bc)/(ab + b2 + ac + bc)

= 2(ab + 2ac + bc)/(ab+ 2ac+ bc) ( since b2 = ac)

= 2

Hence option (3) is the answer.

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