The grandfather’s age is 4 years more than nine times the age of the g

The grandfather’s age is 4 years more than nine times the age of the grandson. The father’s age of 40 years is 2 years less than six times the age of his son. The age of the grandfather is :

77 years
70 years
67 years
63 years
This question was previously asked in
UPSC CAPF – 2009
Let G be the grandfather’s age, F be the father’s age, and S be the son’s age. The son in the second statement is the grandson in the first statement. Let GS denote the grandson’s age, so S = GS.

From the second statement: The father’s age is 40 years.
F = 40
The father’s age (40) is 2 years less than six times the age of his son (GS).
F = 6 * GS – 2
40 = 6 * GS – 2
40 + 2 = 6 * GS
42 = 6 * GS
GS = 42 / 6 = 7 years. The grandson’s age is 7 years.

From the first statement: The grandfather’s age (G) is 4 years more than nine times the age of the grandson (GS).
G = 9 * GS + 4
G = 9 * 7 + 4
G = 63 + 4
G = 67 years.

The age of the grandfather is 67 years.

This is an age problem involving multiple generations. The key is to identify the relationships between the ages and use the known age (father’s age) to find the age of the common person in the two relations (grandson/son), and then use that age to find the age of the grandfather.
Clearly defining variables for each person’s age and carefully translating the word problem into mathematical equations helps avoid errors. The problem assumes the son mentioned in the father-son relationship is the same person as the grandson mentioned in the grandfather-grandson relationship, which is a standard assumption in such problems unless otherwise specified.
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