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Question

A is elder to B by 2 years. A’s father F is twice as old as A and B is twice as old as his sister S. If the age of the father and sister differs by 40 years, find A's age.


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Solution

Step 1: Form a system of equation based on the given statement of problem

Let the present age of A is x,

The present age of B is y,

The present age of F is z

The present age of S is t

According to the question,

A is elder to B by 2 yearsx=y+2................(i)

F is twice as old as Az=2x......................(ii)

B is twice as old as Sy=2t.........................(iii)

The age of the father and sister differ by 40 yearsz-t=40....................(iv)

Step 2: Solve above system of equations

From equation (i) and (iii) we get x=2t+2.......................(v)

From equation (iv) we have t=z-40 put this value in equation (v) we get,

x=2z-40+2x=2z-80+2x=2z-78.........................(vi)

Put value of z from equation (ii) in equation (vi)

x=22x-78x=4x-784x-x=783x=78x=783x=26

Hence, the present age of A is 26 years


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