Maths Shortcuts and Mind Tricks for Age Related Problems Part-II
So here we are again providing you some shortcuts for solving age related problems.
Q.) If the difference between the present age of a father and his son is 14 years & ratio of their ages after 11 years will be 4:3. Then Find the present age of the son.
Solution :-
We are Given
The difference of Present age between father and his son = 14 years.
Ratio of their ages after 11 years = 4 : 3
Shortcut Method:
To solve these types of questions, we can use the below matrix formula:
Difference b/w given Age Ratio ⋯ Difference Age
⋮ ⋱ ⋮
‘Age Ratio’ whose age we have to calculate ⋯ x
So in this case, we have
Difference b/w given Age Ratio = 1 (as given, 4-3 = 1)
Difference Age = 14 years
We have to find the age of the son, so we will take his Age ratio which is = 3.
Let x be the age of the son
So we are provided with three values & we have to find the fourth one. By Substituting all the given three values in the above formula we get,
1 ⋯ 14
⋮ ⋱ ⋮
3 ⋯ x
By Cross Multiply the values, we get
x= 42
This will be the age of the son after 11 years as we have given the age ratio of father and his son after 11 years. So to find the present age of the son we have to subtract 11 from the above calculated age.
i.e The present age of the son, x = ( 42 – 11 ) years.
= 31 years.
Therefore, 31 years is the required answer.
Now, Try to solve the below question:
Q) Seema is younger than Mira by 4 years. If the ratio of their ages is 7:9 respectively then what is the present age of the Seema?
Solution:
According to the Formula, we have
Difference b/w given Age Ratio ⋯ Difference Age
⋮ ⋱ ⋮
‘Age Ratio’ whose age we have to calculate ⋯x
By Substituting the given values in the above formula, we get
2 ⋯ 4
⋮ ⋱ ⋮
7 ⋯ x
By Cross Multiply the given values in the matrix format, we get
2x= 28
i.e x= 14 years.
Therefore, the required Age of the Seema is 14 years.
Thank You Friends !!
Keep Learning !