Madhu is thirteenth from the end in a column of girls. There were thrice as many in front of her as there were behind. How many girls are there between Madhu and the fifth girl from the front of the column?

31

The correct answer is Option (1) → 31

Step 1: Let’s define the number of girls

Let x = number of girls behind Madhu.

According to the problem, the number in front of Madhu = 3 × number behind her = 3x

Madhu’s position from the front = number in front + 1 = 3x + 1

Madhu’s position from the end = total girls − position from front + 1

Given, Madhu is 13th from the end:

$\text{Total girls} - (3x + 1) + 1 = 13$

$\text{Total girls} - 3x = 13$

$\text{Total girls} = 3x + 13$

Step 2: Relate x and total number of girls

Number behind Madhu = x

But number behind Madhu = total girls − position from front = (3x + 13) − (3x + 1) = 12

$x = 12$

Step 3: Total number of girls

$\text{Total girls} = 3x + 13 = 3(12) + 13 = 36 + 13 = 49$

Step 4: Madhu’s position from front

$\text{Position from front} = 3x + 1 = 3(12) + 1 = 37$

Step 5: Fifth girl from front

Position = 5

Number of girls between Madhu and 5th girl:

$37 - 5 - 1 = 31$