Question

Mohan’s mother is six times as old as Mohan now, Five years after, she will be $20$ years older than Mohan. What are their present ages?
A. $Mohan = 9,mother = 29$
B. $Mohan = 4,Mother = 24$
C. Mohan$ = 5,mother = 30$
D. Mohan $ = 10,mother = 60$

Answer 1

Hint: We will suppose the age of Mohan then we will apply the first condition and then we will convert their present age into after $5$ years. Further we will apply the second condition. Further we will find their present ages.


Complete step by step solution:
 Let the age of mohan $ = x$ years
Let his mother’s age be $ = 6x$ years
After $5$ years,
Mohan age $ = (x + 5)years$
Mohan’s mother age $ = (6x + 5)years$
According to the given information in the question, we have
$(x + 5) + 20 = 6x + 5$
$ \Rightarrow 6x + 5 - n - 5 - 20 = 0$
$ \Rightarrow 6x - x - 20 = 0$
$ \Rightarrow 5x - 20 = 0$
$ \Rightarrow 5x = 20$
$ \Rightarrow x = \dfrac{{20}}{5}$
$ \Rightarrow x = 4$
$\therefore $Mohan age $ = 4$ years
And mohan’s mother age $ = 6 \times 4years$
Mohan’s mother’s age $ = 24$ years
Hence, the correct option is B.


Note: Students keep in mind that when we will apply the condition, then add , subtract or multiply by a smaller number to have the same balance.