Question

What is Ravi’s present age?
I.The present age of Ravi is half of that of his father.
II. After 5 years, the ratio of Ravi’s age to that of his father's age will be 6:11.
III. Ravi is 5 years younger than his brother.
a)I and II only
b)II and III only
c)I and III only
d) All I, II and III
e)Even with all the three statements, the answer cannot be determined.

Answer 1

Hint: From three equations with the involving three variables i.e. Ravi’s age, his father, his brother. Now try to get the minimum equations to get the value of Ravi’s age. Don’t involve unnecessary variables to form complex equations. Use only one variable for one quantity.

Complete step-by-step answer:

Here, we need to find the present age of Ravi by using suitable statements.
So, as we can see that Ravi, his father and his younger brother are involved within the statement given in the question. Now suppose the present age of Ravi be ‘x’ years, his father’s age be ‘y’ years and his younger brother’s age be ‘z’ years.
Now, let’s form the mathematical equations to solve them and get the value of x. So the first statement is given as the present age of Ravi is half of his father. So we can get the equation in x and y variable as
$x=\dfrac{y}{2}.............\left( i \right)$
Now, the second statement is given that after 5 years the ratio of Ravi’s age to his father’s age will be 6:11. So, Ravi’s age after 5 years = x + 5 and his father’s age after 5 years = y + 5.
Now, it is given that the ratio of their age after 5 years is 6:11. Hence, we get
$\dfrac{x+5}{y+5}=\dfrac{6}{11}$
On cross multiplying the above equation, we get
11x + 55 = 6y + 30
11x – 6y + 25 = 0…………….(ii)
And the third equation with the help of the third line can be given as x = z – 5, as the third statement is given as Ravi is 5 years younger than his brother. So, we get
x = z – 5………………(iii)
Now, we can observe that the first two equations are in x, y variables. And (x, y) are the ages of Ravi and his father respectively. So, we can solve them and get their ages. As z is not involved anywhere else. And we don’t require ‘z’ as well. So, we can get the age of Ravi by using I and II statements only.
Put $x=\dfrac{y}{2}$ in equation (ii), we get $11\times \dfrac{y}{2}-6y+25=0$
11y – 12y + 50 = 0
y = 50 years
Hence, $x=\dfrac{y}{2}=\dfrac{50}{20}=25$ years. So, we can calculate age of Ravi by using statements I and II only
So, option (a) is correct.

Note: One may tick option I, II and III only as the correct option. But we need to minimize the statements to get the ae of Ravi. So, we don’t need the statement III. Hence option (I, II) is the correct one. We don’t need to solve both the equations, we have done for understanding the question in an easier way. Don’t make equations wrong with the statements and use the same variable for a single quantity in all three cases for the flexibility of the solution.