Question

There are two friends. They are in different cities.The first friend come back to his village after 15 days and the second friend comes back to his village after 75 days and they met on February 2. In which month and day will they meet again?

Answer 1

The friends come to oillagie after 15 & 75 days respatively.
They meet on 2nd feb.

You can see here, that they meet after every 75 days,
i.e. the LCM of 75 & 15.
So, if they meet on 2nd Feb, they will meet after 75 days, again, i.e. on-
Case - I $\to$ If Feb is of 28 days.
$\underset{\underset{Feb}{\downarrow }}{26}+\underset{\underset{Mar}{\downarrow }}{31}+\underset{\underset{April}{\downarrow }}{18}\Rightarrow {18}^{th}April$
Case II $\to$ If Feb is of 29 days.
$\underset{\underset{Feb}{\downarrow }}{27}+\underset{\underset{Mar}{\downarrow }}{31}+\underset{\underset{April}{\downarrow }}{17}\Rightarrow {17}^{th}April$ no. of days