Age Maze!!

Algebra Level 2

My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 120 years. Can you tell me my age in years ?


The answer is 72.

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5 solutions

Vishal Rai
Oct 1, 2014

All you have to do is take the ages of the Grandson, Son and the Father, in years as x, y and z, respectively.

According to condition 1:

365 * z = y * 52

So, y = ((365 * z ) / 52) [equation 1]

Note: 1 year has 365 days and 52 weeks.

According to condition 2:

x = (12 * z) [equation 2]

Note: 1 year has 12 months.

Going by the data:

x + y + z = 120

So, (12 * z) + ((365 * z) / 52) + z = 120 [replacing y & z from 1 and 2]

z * ( 12 + 365/52 + 1) = 120

z * ( 624 + 365 + 52 ) / 52 = 120

z * (1041)/52 = 120

Solving for z, z = 210 * 52 / 1041 = 5.99 = 6

Therefore, x = 12 * z = 6 * 12 = 72 [equation 2]

So, Grandpa's age is 72 years.

Sorry, I don't know how to do the text editing, as I am new to posting solutions.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

x-grandson's age
y-son's age
z-grandfather's age
x+y+z=120
7x=y
12x=z
substitute the value of y and z in the equation in terms of x
x+7x+12x=120
20x=120
x=6
z=12x=12(6)
z=72



1 Helpful 0 Interesting 0 Brilliant 0 Confused
Lew Sterling Jr
Oct 21, 2014

x+y+z = 120

7x = y

12x = z

x + 7x + 12x = 120

20x = 120

x = 6

12x = z

12(6) = z

72 = z

1 Helpful 0 Interesting 0 Brilliant 0 Confused

g = grandson's age s = son's age m = my age : "My grandson is about as many days as my son is weeks," s = 7g : my grandson is as many months as I am in years. m = 12g : g + s + m = 120 Substitute for m and s g + 7g + 12g = 120 20g = 120 g = 120%2F20 g = 6 yrs is grandson's age EASY !! AYAYA ^_^ :P

Shubham Verma - 6 years, 7 months ago

Let X be the age of the grandson, Y be the age of the son and Z be the age asked.

x+y+z = 120.

7 days are equal to 1 week --> 7x = y.

12 months equal to 1 year --> 12x = z.

Using first equation:

x+7x+12x = 120 --> 20x = 120 ---> x = 6.

Back to third equation: 12x = z

z = 72.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

The grandson's age is X. His father is 7 times older than him, 7X. His grandmother is 12 times older than him, 12X. X + 7X + 12X = 20X = 120 ====> X = 6. His grandmother is then 6*12 = 72.

Daniel Sass - 6 years, 8 months ago
Jabale Rahmat
Oct 29, 2014

Let the age of the grandson is x.

Therefore, the age of the son is 7x, as 1 week = 7 days.

The age of the grandfather is equal to 12x as one year equals to 12 months.

Sum of their ages is x + 7x + 12x =120 so, solving this, the value of x is 6. so the age of the grandfather is 6*12 = 72 years... :) :) :)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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