Question
The ratio of ages of A and B is 4:5 and that of B and C
is 3:2. Find the age of B after 10 years. Statement I: Difference between the ages of C and A after 10 years and the difference between ages of A and B after 10 years is same. Statement II: Difference between ages of A and C is 4 years. Each of the questions given below has one question and two statements marked I and II. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer.Solution
ATQ,
We are given: The ratio of ages of A and B 4:5. The ratio of ages of B and C is 3:2. We are tasked with finding B's age after 10 years. Let:
A's age = 4x B's age = 5x, C's age = 10x/3.
Statement I The difference between the ages of C and A after 10 years is the same as the difference between the ages of A and B after 10 years. This implies: (C+10)−(A+10)=(B+10)−(A+10). C−A=B−A. Substituting the values in terms of x: 
Solving for x determines A,B, and C's ages. Statement I is sufficient.
The difference between C and A is 4 years: C − A = 4. Substituting values: 
Simplify: 
Solving for x determines A,B, and C's ages. Statement II is sufficient.
Either Statement I or II alone is sufficient.
Solve the quadratic equations and determine the relation between x and y:
Equation 1: x² - 40x + 300 = 0
Equation 2: y² - 30y + 216 = 0
I. 3x2 = 2x2 + 9x – 20
II. 3y2 = 75
I. 15/(√x)+9/(√x)=11√x
II. (√y)/4 + (5√y)/12 = 1/(√y)
I. 6x² + 37x + 45 = 0
II. 3y² - 11y + 6 = 0
I. x2 – 13x + 40 = 0
II. 2y2 – 15y + 13 = 0Â
I. 3p² - 11p + 10 = 0
II. 2q² + 13q + 21 = 0
I. 63x² + 146x + 80 = 0
II. 42y² + 109y + 70 = 0
I. 35x² - 24x – 35 = 0
II. 72y² - 145y + 72 = 0
Solve the quadratic equations and determine the relation between x and y:
Equation 1: x² - 24x + 135 = 0
Equation 2: y² - 26y + 153 = 0
I. 5x² -14x + 8 = 0 Â
II. 2y² + 17y + 36 = 0  Â
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