Two numbers are such that the square of one is 224 less than 8 times the square of the other. If the numbers are in the ratio of 3 : 4, then their values are = ?
A. 12, 16
B. 6, 8
C. 9, 12
D. 12, 9
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & {\text{Let number be }}x\,\&\, y \cr & {\text{Given,}} \cr & \,\,x:y \cr & \,\,\,\,3:4 \cr & \,3a:4a \cr & {\text{Now , given that}} \cr & \Rightarrow {\text{8}}{\left( {3a} \right)^2} = {\left( {4a} \right)^2} + 224 \cr & \Rightarrow 72{a^2} = 16{a^2} + 224 \cr & \Rightarrow 56{a^2} = 224 \cr & \Rightarrow {a^2} = 4 \cr & \Rightarrow a = 2 \cr & {\text{Numbers are}} \cr & x = 3 \times 2 = 6 \cr & y = 4 \times 2 = 8 \cr} $$Related Questions on Ratio
If a : b : c = 3 : 4 : 7, then the ratio (a + b + c) : c is equal to
A. 2 : 1
B. 14 : 3
C. 7 : 2
D. 1 : 2
If $$\frac{2}{3}$$ of A=75% of B = 0.6 of C, then A : B : C is
A. 2 : 3 : 3
B. 3 : 4 : 5
C. 4 : 5 : 6
D. 9 : 8 : 10
Join The Discussion