321.
If x2 + 4y2 = 4xy, then x : y is -
- (A) 1 : 1
- (B) 1 : 2
- (C) 2 : 1
- (D) 1 : 4
Solution:
$$\eqalign{ & = {x^2} + 4{y^2} = 4xy \cr & \Rightarrow {x^2} - 4xy + 4{y^2} = 0 \cr & \Rightarrow \left( {x - 2{y^2}} \right) = 0 \cr & \Rightarrow x = 2y \cr & \Rightarrow \frac{x}{y} = 2 \cr & \Rightarrow x:y = 2:1 \cr} $$
322.
Harsha is 40 years old and Ritu is 60 years old. How many years ago was the ratio of their ages is 3 : 5 ?
- (A) 10 years
- (B) 20 years
- (C) 37 years
- (D) 5 years
Solution:
$$\eqalign{ & {\text{Harsha = 40}} \cr & {\text{Ritu = 60}} \cr & \frac{{{\text{Harsha}}}}{{{\text{Ritu}}}} = \frac{{40}}{{60}} \cr} $$ ∴ Let x years ago their ages ratio was 3 : 5 $$\eqalign{ & \Rightarrow \frac{{40 - x}}{{60 - x}} = \frac{3}{5} \cr & \Rightarrow 200 - 5x = 180 - 3x \cr & \Rightarrow 2x = 20 \cr & \Rightarrow x = 10 \cr} $$