Question

Out of the total number of players, 100/3 % are in hotel X and the remaining are in hotel Y. If 20 players from hotel Y are shifted to hotel X, then the number of players in hotel X becomes 50% of the total number of players. If 20 players from hotel X are shifted to hotel Y, then the number of players in hotel X becomes what per cent of the total number of players?
1. 20.67%
2. 16.67%
3. 26.34%
4. 12.75%

Answer 1

Correct Answer - Option 2 : 16.67%

Let total players = A

Players in Hotel X = 100/3% of A = A/3

Players in Hotel Y = A - A/3 = 2A/3

According to question:

A/3 + 20 = 50/100 × A

⇒ A/3 + 20 = A/2

⇒ A/2 - A/3 = 20

⇒ A/6 = 20

⇒ A = 20 × 6

⇒ A = 120

Now, if 20 players from hotel X are shifted to hotel Y, then the number of players in hotel X becomes (A/3 - 20) = 120/3 - 20 = 40 - 20 = 20

And the number of players in hotel X becomes what percent of the total number of players:

20/120 × 100

= 16.67%

Hence, ‘16.67%’ is the correct answer.