Sam owns a football accessory shop. At present, the number of items in his shop is 2000 and every year, he plans to increase it by 10% every year. After 2 years, he decides to open 10 more shops and distributes the total number of items he has in such a way that total items of no shop are greater than 20% of the total items of any other shop. What is the approximate maximum possible number of items in a shop?
A. 200
B. 216
C. 220
D. 230
E. 260
Given: Sam owns a football accessory shop. At present, the number of items in his shop is 2000 and every year, he plans to increase it by 10% every year. After 2 years, he decides to open 10 more shops and distributes the total number of items he has in such a way that total items of no shop are greater than 20% of the total items of any other shop.
Asked: What is the approximate maximum possible number of items in a shop?
At present, the number of items in his shop = 2000
he plans to increase it by 10% every year.
Next year, the number of items in his shop will be = 2000 * 1.1 = 2200
Second year, the number of items in his shop will be = 2200 * 1.1 = 2420
After 2 years, the number of shops he will have = 1 + 10 = 11 shops
He distributes the total number of items he has in such a way that total items of no shop are greater than 20% of the total items of any other shop.
If all other shops have number of items = x => Total number of items in 10 shops = 10x
Then the maximum number of items in 11th shop < 1.2x
Total no of items in 11 shops approximately = 10x + 1.2x = 11.2x
But total no of items in 11 shops = 2420
11.2x = 2420
x = 2420/11.2
1.2x = 2420/11.2*1.2 = 260 approx
Maximum no of items a shop may have = 260 since no of items is a positive integer.
IMO E