the present age of a father and his son are in the ratio 10:3. if the son is 15 years old now, in how many years will the ratio of their age be 2:1?
present:
father --- 10x
son -------3x
3x = 15
x = 5
son is now 15 and father is now 50
in t years,
(50+t)/(15+t) = 2/1
30+2t = 50+t
t = 20
in 20 years , the father will be 70 and the son will be 35
(which is in the ratio of 2:1 )
The arithmetic mean of x y and z is 6 while x y z t u v and w is 9 calculate the arithmetic mean of t u v and w.
To solve this problem, we first need to find the present age of the father. We know that the present age ratio of the father to the son is 10:3.
Let's assume the present age of the father is 10x and the present age of the son is 3x. According to the given information, the age of the son is 15. Hence, 3x = 15.
Now, we can solve for x by dividing both sides of the equation by 3:
3x/3 = 15/3
x = 5
Therefore, the present age of the father would be:
10x = 10 * 5 = 50
Now, let's find the number of years required for the ratio of their ages to become 2:1. At present, the ratio of their ages is 10:3, and we want to find out how many years it will take for this ratio to become 2:1, which means the new ratio of their ages will be 2x:1x.
Let's assume it takes 'y' years for the ratio to become 2:1. So, after 'y' years, the age of the father will be 50 + y and the age of the son will be 15 + y.
Now, let's set up an equation based on the given ratio:
(50 + y)/(15 + y) = 2/1
To solve this equation, we can cross-multiply:
2(15 + y) = 1(50 + y)
30 + 2y = 50 + y
Next, let's isolate 'y' by subtracting 'y' from both sides of the equation and subtracting 30 from both sides:
2y - y = 50 - 30
y = 20
Therefore, it will take 20 years for the ratio of their ages to become 2:1.