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In a group of 400, every student specialises in exactly two dance forms from Salsa, Belly, Hip-Hop and Ballet. It is known that 100 students specialise in Salsa and Belly dancing, 70 students specialise in Salsa and Hip-Hop dancing, while 50 students specialise in Belly and Hip-Hop dancing. Among the remaining students, an equal number specialise in each of the other possible dual dance categories.
 
Q. If 80% of all the possible dual categories are selected for stage show in Berlin, then how many of the performers are bound to perform in Berlin?
  • a)
     300
  • b)
     320
  • c)
    360
  • d)
    200
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In a group of 400, every student specialises in exactly two dance form...
The total of all the possible dual categories is 400 and 80% of 400 is 320.
Hence, option 2.
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Most Upvoted Answer
In a group of 400, every student specialises in exactly two dance form...
Total duals
1. Salsa+ Belly =100
2. Salsa + Hip hop =70
3.Belly+ hip hop =50
4. salsa+ ballet =60
5. ballet+ belly =60
6. ballet + hip hop =60

given no. 1+2+3 = 220
an d rest = 400-220 = 180 divided equally in 4 5,6 as 60

80% of possible duals..
total duals = 1+2+3+4+5+6 = 400
80% of 400 = 320
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In a group of 400, every student specialises in exactly two dance form...
To solve this problem, we can use a Venn diagram to represent the given information. Let's label the four dance forms as S (Salsa), B (Belly), H (Hip-Hop), and V (Ballet).

Let's start by filling in the information we have:

- 100 students specialize in Salsa and Belly dancing (S ∩ B)
- 70 students specialize in Salsa and Hip-Hop dancing (S ∩ H)
- 50 students specialize in Belly and Hip-Hop dancing (B ∩ H)

We know that every student specializes in exactly two dance forms, so the total number of students is 400. Let's denote the number of students who specialize in both Belly and Ballet dancing as x. Since an equal number of students specialize in each of the other possible dual dance categories, the number of students who specialize in both Salsa and Ballet dancing is also x.

Now, let's fill in the remaining information:

- 100 students specialize in Salsa and Belly dancing (S ∩ B)
- 70 students specialize in Salsa and Hip-Hop dancing (S ∩ H)
- 50 students specialize in Belly and Hip-Hop dancing (B ∩ H)
- x students specialize in Belly and Ballet dancing (B ∩ V)
- x students specialize in Salsa and Ballet dancing (S ∩ V)

We know that the total number of students is 400. Therefore, the sum of the number of students in each region of the Venn diagram should equal 400. Let's write an equation to express this:

100 + 70 + 50 + x + x = 400

Simplifying the equation, we have:

220 + 2x = 400

Subtracting 220 from both sides, we get:

2x = 180

Dividing both sides by 2, we find:

x = 90

Now that we know the value of x, we can determine the number of students who specialize in both Salsa and Ballet dancing (S ∩ V) and the number of students who specialize in both Belly and Ballet dancing (B ∩ V). Both of these values are equal to x, which is 90.

Finally, to find the number of performers bound to perform in Berlin, we need to calculate 80% of all the possible dual categories. Since there are 4 dual categories (S ∩ B, S ∩ H, B ∩ H, and S ∩ V), 80% of this is:

4 * 80% = 3.2

Rounding to the nearest whole number, we get 3. Therefore, 3 dual categories will be selected for the stage show in Berlin.

Since each dual category represents two dance forms, the total number of performers bound to perform in Berlin is:

3 * 2 = 6

So, the correct answer is 6 performers, which corresponds to option B.
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In a group of 400, every student specialises in exactly two dance forms from Salsa, Belly, Hip-Hop and Ballet. It is known that 100 students specialise in Salsa and Belly dancing, 70 students specialise in Salsa and Hip-Hop dancing, while 50 students specialise in Belly and Hip-Hop dancing. Among the remaining students, an equal number specialise in each of the other possible dual dance categories.Q. If 80% of all the possible dual categories are selected for stage show in Berlin, then how many of the performers are bound to perform in Berlin?a)300b)320c)360d)200Correct answer is option 'B'. Can you explain this answer?
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