Question

Every 8th person that goes into a store gets a free bottle. Every 10th person that goes into a store gets a t-shirt. There are 100 bottles and 100 t shirts to give out. How many people get a t shirt and a bottle

Answer 1

25 persons will get both bottle and t – shirt.

Solution:

Given, every 8th person that goes into a store gets a free bottle.  

And every 10th person that goes into a store gets a t-shirt.  

There are 100 bottles and 100 t shirts to give out.  

We have to find how many people get a t shirt and a bottle

Now, as there are 100 t- shirts, last person to get t – shirt is:

10 x 100 = 1000th person will get last t – shirt

We have to find lcm of 8 and 10, to know who gets both bottle and t – shirt.

So, L.C.M of 8 and 10 = lcm(8, 10)  

= 2 x lcm(4, 5)  

= 2 x 4 x 5 [ as no common factors available for 4 and 5 ]

= 40

So, every 40th person will get both bottle and t – shirt.

Then, out of 1000 people, number of people who get both bottle and t – shirt = $\frac{1000}{40} = 25$