B is 3 years older than A and B is also 3 years younger than ‘C’. 3 years hence, the respective ratio between the ages of A and C will be 4: 5. What is the sum of the present ages of A, B and C?a)48 yearsb)56 yearsc)63 yearsd)84 yearse)72 yearsCorrect answer is option 'E'. Can you explain this answer?

Question

B is 3 years older than A and B is also 3 years younger than &lsquo;C&rsquo;. 3 years hence, the respective ratio between the ages of A and C will be 4: 5. What is the sum of the present ages of A, B and C?a)48 yearsb)56 yearsc)63 yearsd)84 yearse)72 yearsCorrect answer is option 'E'. Can you explain this answer?

Answer

Let B age = b

so A age = b-3

and C age = b+3

(A+B+C)present age = 3b

3 years later A age = b and C age = b+6

given( A age) / (C age)=4:5

so b : b+6 =4:5

or 5b=4b+24

or b=24

since question is asking for (A+B+C) present age

so (A+B+C) present age =3b

or 3*24=72

therefore option E is correct

Answer

C. To find the exact ages of A, B, and C, we need more information.

We can set up two equations based on the given information:

B = A + 3 (B is 3 years older than A)
B = C - 3 (B is 3 years younger than C)

We can use substitution to solve for one of the variables. Since we have two equations for B, we can set them equal to each other:

A + 3 = C - 3

Simplifying, we get:

A + 6 = C

Now we can substitute this expression for C in one of the original equations:

B = C - 3
B = (A + 6) - 3
B = A + 3

So we have two equations for A and B:

B = A + 3
B = C - 3

And we know that C = A + 6. We can substitute this expression for C in the second equation:

B = (A + 6) - 3
B = A + 3

So we have the same equation for B in both cases. This means that we don't have enough information to determine the exact ages of A, B, and C. We can only say that B is 3 years older than A and 3 years younger than C.

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