Question

At present Anil is 1.5 times of Purvi’s age. 8 years later, the respective ratio between Anil and Purvi’s ages will be 25:18. What is Purvi’s present age?
(a) 50 yr
(b) 28 yr
(c) 42 yr
(d) 36 yr

Answer 1

Hint: Let the ages of Purvi and Anil be x years and y years, respectively. Then use the conditions given in the question to form two equations one for the present age and one for the age 8 years later. For 8 years later, the ages would be x+8 and y+8. Solve the equations to get the value of x, i.e., the age of Purvi.

Complete step-by-step answer:
To start with the question, we let the present ages of Purvi and Anil be x years and y years, respectively.
Now it is given in the question that the age of Anil is 1.5 times the present age of Purvi. So, if we represent this in form of equation, we get
$y=1.5x......(i)$
Also, it is given that 8 years from now, i.e., when the age of Purvi is (x+8) years and Anil is (y+8) years old, the respective ratio between Anil and Purvi’s ages will be 25:18. So, if we use the fractional form of a ratio and combine it with the given statement, we get
$\dfrac{y+8}{x+8}=\dfrac{25}{18}$
Now we will use equation (i) to substitute the value of y. On doing so, we get
$\dfrac{1.5x+8}{x+8}=\dfrac{25}{18}$
Now we will cross-multiply and solve the equation.
$18\left( 1.5x+8 \right)=25(x+8)$
$\Rightarrow 18\times 1.5x+18\times 8=25x+25\times 8$
$\Rightarrow 27x-25x=25\times 8-18\times 8$
$\Rightarrow 2x=56$
$\Rightarrow x=28 years$
Therefore, the answer to the above question is option (b).

Note: Be very careful while using the ratio, as the order of ratio is very important and can give different results and interpretation if used in the wrong order. Also, remember that after the passage of eight years the values of x and y are not changed, they are fixed. You need to add 8 to both of them to show their respective ages 8 years from the present time. In this type of questions, we must always fix the present ages for easy understanding. Some students also try to take the age 8 years later as x and y, then they obtain the present age as x=8 and y = 8. This will complicate the solution unnecessarily.