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CLAT Exam  >  CLAT Questions  >   10 Girls and 9 boys are standing in a line. ... Start Learning for Free
10 Girls and 9 boys are standing in a line. No two boys and no two girls are standing together. Neha is standing 4th to the left of Megha. If all the boys are removed then Neha is 7th from the right end. Find the position of Megha from the left end among 19 students.
  • a)
    10th
  • b)
    9th
  • c)
    11th
  • d)
    12th
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
10 Girls and 9 boys are standing in a line. No two boys and no two gi...
No two boys and no two girls are standing together means the sequence will be girl, boy, girl, boy...
If all the boys are removed then Neha is 7th from the right end. Among all the 19s Neha is 13th (7 girls +6 boys) from the right end.
Neha is standing 4th to the left of Megha it means Megha is standing 4th to the right of Neha.
So Megha is 9th (13-4) from the right end.
The position Megha from the right end = (total student – position from right end + 1)
=19-9+1
=11th
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10 Girls and 9 boys are standing in a line. No two boys and no two gi...
Solution:

Given data:

Total number of students = 10 girls + 9 boys = 19

Neha is standing 4th to the left of Megha.

If all the boys are removed then Neha is 7th from the right end.

Approach:

Let us assume that all the girls are standing together in a line and all the boys are standing together in a line. Now, we can arrange these two lines in such a way that no two girls and no two boys are standing together.

Let us first arrange the girls in a line. There are 10 girls, so there are 10! ways to arrange them. However, if we consider the arrangement of girls as a block, we can arrange the block and the boys in a line in (10! × 11!) ways.

Now, Neha is standing 4th to the left of Megha. Let us assume that Megha is standing at position x from the left end. Then, Neha is standing at position x + 4 from the left end.

If all the boys are removed, then there are 10 girls standing in a line. Neha is 7th from the right end. Therefore, Neha is standing at position 10 - 7 + 1 = 4 from the left end.

Now, we can use these two equations to find the value of x.

x + 4 = (10! × 11!) / 19

x = (10! × 11!) / 19 - 4

x = 5 × 10! × 11! / 19

x = 11!

Therefore, Megha is standing at position 11 from the left end among 19 students.

Hence, the correct answer is option (c) 11th.
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10 Girls and 9 boys are standing in a line. No two boys and no two girls are standing together. Neha is standing 4th to the left of Megha. If all the boys are removed then Neha is 7th from the right end. Find the position of Megha from the left end among 19 students.a)10thb)9thc)11thd)12thCorrect answer is option 'C'. Can you explain this answer?
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