Question

A school bus picking up children in a colony of flats stops at every sixth block of flats. Another school bus starting from the same place stops at every eighth block of flats. Which is the first bus stop at which both of them will stop?

Answer 1

Hint: At first, we find out which blocks the first bus stops. Since it stops at every sixth block, its corresponding blocks will be ${{6}^{th}},{{12}^{th}},{{18}^{th}},{{24}^{th}},{{30}^{th}},{{36}^{th}}$ and so on. Then, we find out which blocks the second bus stop. Since it stops at every eighth block, its corresponding blocks will be ${{8}^{th}},{{16}^{th}},{{24}^{th}},{{32}^{th}},{{40}^{th}}$ and so on. Finding out the first common will give us the answer.

Complete step by step answer:
In this problem, we are told that there are two school buses present. Both of them pick up children from a colony of flats. But, the picking style of the buses are different. The first bus stops at every sixth block of flats and picks up, while the second bus stops at every eighth block of flats and picks up. Both of them start from the same place.
Now, we need to find that which blocks the first bus stops. Since it stops at every sixth block, its corresponding blocks will be,
Bus $1$ : ${{6}^{th}},{{12}^{th}},{{18}^{th}},{{24}^{th}},{{30}^{th}},{{36}^{th}}$ and so on
Now, we need to find that which blocks the first bus stop. Since it stops at every sixth block, its corresponding blocks will be,
Bus $2$ : ${{8}^{th}},{{16}^{th}},{{24}^{th}},{{32}^{th}},{{40}^{th}}$ and so on
If we compare their stops, then we can see that the \[{{24}^{th}}\] block is the first common.
Thus, we can conclude that the first bus stop at which both of them will stop is the \[{{24}^{th}}\] block.

Note: We can also solve the problem in a more textbook way. We see that the stops of the first bus are nothing but multiples of $6$ and that of the second bus are multiples of $8$ . So, their first common stop will be the LCM of $6$ and $8$ which is $24$.