Question

Forty students are standing in a single row such that after the first boy, there is one girl. After the second boy, there are two girls. After the third boy, there are three girls and so on. Work out the number of girls in the second-half of the row.

Answer 1

Answer:

18 girls

Step-by-step explanation:

The arrangement can be given as :

B+G+B+2G+B+3G+B+4G+B+5G+B+6G+B+7G+B+5G= 40 Students.

So number of girls in the second half of the row = 6+7+5=18.

Answer 2

Answer:

The correct answer is : 17

Step-by-step explanation:

Let the number of boys in the row be x. Then, the number of girls in the row is 40 - x. So, there are x - 1 places where a boy can stand. So, there are x - 2 places where a boy can stand. Similarly, after the third boy, there are three girls. So, there are x - 3 places where a boy can stand. Continuing this pattern, we get the equation:

(x-1) + (x-2) + (x-3) + ... + 2 + 1 = 40 - x

Simplifying this equation, we get:

x(x-1)/2 = 20

x(x-1) = 40

On solving this quadratic equation, we get $x = 6$ or $x = -7$. Since we cannot have negative number of boys, we take x = 6. Therefore, the number of girls in the row is 40 - x = 40 - 6 = 34. Since there are 20 places before the 6th boy, there are 14 places after the 6th boy. Out of these 14 places, the first 6 places are occupied by boys. Therefore, the number of girls in the second-half of the row is 14 - 6 = 8. But we need to add the number of girls after  6th boy. From the given pattern, after the 6th boy, there are 9 girls. Therefore, the total number of girls in the second-half of the row is 8 + 9 = 17.

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