Quantity I Present ages of A and B are in the ratio of 4 5 respectively Present ages of C and D are ...........

Quantitative Aptitude(IBPS RRB PO) Arithmatic inequalities

Direction: Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers.

Quantity I: Present ages of A and B are in the ratio of 4: 5 respectively. Present ages of C and D are in the ratio of 5: 6 respectively. The present average age of A, B, C and D is 40 years and 6 months. Age of A after 2 years will be half the age of D 6 years hence. Find the present average age of B and C.

Quantity II: 39 years

Quantity I > Quantity II

Quantity I < Quantity II

Quantity I ≥ Quantity II

Quantity I ≤ Quantity II

Quantity I = Quantity II or No relation

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Explanation:

Quantity I:
Let the present ages of A and B are 4x and 5x years respectively and the present ages of C and D are 5y and 6y years respectively.
So, sum of the ages of A, B, C and D = 4x + 5x + 5y + 6y = 40.5 x 4
So, 9x + 11y = 162
Also given that,
2 x (4x+2) = 6y + 6
So, 4x – 3y = 1
From both the equation, we get,
x = 7 and y = 9
So, the present ages of A, B, C and D are 28,
35, 45 and 54 respectively.
Present average age of B and C =(35+45)/2=40years
Quantity II: 39
Therefore, Quantity I >Quantity II