Question

Five years from when Ram was 5 year old, Shyam was 5 times the age of Ram. Present age of Shyam is 3 times that of Ram. Find the present age of Ram and Shyam.
(a) 10, 30
(b) 20, 60
(c) 30, 90
(d) 15, 45

Answer 1

Hint: Assume that the present age of Ram is x year and the present age of Shyam is y year. Then apply the conditions according to the question to form equations and solve them.

Complete step-by-step solution:
Let us assume that the present age of Ram is x year.
The present age of Shyam is y year.
It is given in the question that the present age of Shyam is 3 times that of Ram.
That means if we multiply the present age of Ram, that is x, by 3 we will get the present age of Shyam, that is y.
Therefore the equation will be,
$3x=y.....(1)$
The other condition that is given in the question is five years back from now the age of Ram was 5 year.
That means if we subtract 5 from Ram’s present age, we will get 5. Therefore,
$x-5=5$
We will take -5 from left hand side to right hand side to get the value of x.
$\Rightarrow x=5+5=10$
Therefore the present age of Ram is 10 year.
Now if we put the value of x in equation (1) we will get,
$y=3\times 10=30$
Hence, the present age of Ram is 10 year and the present age of Shyam is 30 year.
Therefore, option (a) is correct.

Note: Alternatively we can solve this problem just by cross checking the options. The first condition is five years back from now Ram’s age 5. That means now Ram’s age is 5 + 5 = 10.
Only option (a) has the value 10 as Ram’s age and it is satisfying the other conditions also. Hence, option (a) is correct.