Problem Solving

BTGModeratorVI wrote: ↑

Thu Jul 23, 2020 6:30 am

The present age of a father is 3 years more than three times the age of his son. Three years hence , father's age will be 10 years more than twice the age of the son. Present age of the father is..

A. 9
B. 10
C. 30
D. 33
E. 35

Answer: D
Source: Grockit

Say father's age = x years and son's age = y years

=> x = 3y + 3 ---(1);

Three years hence...

x + 3 = 2(y + 3) + 10

x = 2y + 13 ---(2)

From (1) and (2), we get y = 10 and x = 33

Correct answer: D

Hope this helps!

-Jay
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BTGModeratorVI wrote: ↑

Thu Jul 23, 2020 6:30 am

The present age of a father is 3 years more than three times the age of his son. Three years hence , father's age will be 10 years more than twice the age of the son. Present age of the father is..

A. 9
B. 10
C. 30
D. 33
E. 35

Answer: D

Solution:

We can let F = the present age of the father and S = the present age of the son and create the equations:

F = 3S + 3

and

F + 3 = 2(S + 3) + 10

Substituting 3S + 3 for F in the second equation, we have:

3S + 3 + 3 = 2(S + 3) + 10

3S + 6 = 2S + 6 + 10

S = 10

Therefore, the present age of the father is F = 3(10) + 3 = 33.

Answer: D

BTGModeratorVI wrote: ↑

Thu Jul 23, 2020 6:30 am

The present age of a father is 3 years more than three times the age of his son. Three years hence , father's age will be 10 years more than twice the age of the son. Present age of the father is..

A. 9
B. 10
C. 30
D. 33
E. 35

Answer: D
Source: Grockit

The present age of a father is 3 years more than three times the age of his son
Let x = the PRESENT age of the son
So, 3x + 3 = the PRESENT age of the father

So, x + 3 = the son's age IN THREE YEARS
And 3x + 3 + 3 = the father's age IN THREE YEARS

Three years hence , father's age will be 10 years more than twice the age of the son
In other words: (father's age in 3 years) = 2(son's age in 3 years) + 10
In other words: (3x + 3 + 3) = 2(x + 3) + 10
Simplify: 3x + 6 = 2x + 16
Subtract 2x from both sides: x + 6 = 16
Subtract 6 from both sides: x = 10

This means the son's PRESENT age is 10 years old
Since 3x + 3 = the PRESENT age of the father, the father's present age = 3(10) + 3 = 33

Answer: D

Cheers,
Brent