Some students were standing in a row facing North. Only Deepa was between Sonam and Nada. Bhupendra was exactly midway in the row. The number of students to the left of Bhupendra was equal to the cube of Kalika's rank from the left end and the number of students of the right of Bhupendra was equal to the square of Ashish's rank from the left end of the row. The number of students was less than 1000. How many students were there between Kalika and Bhupendra?
1) 61
2) 60
3) Data Inadequate
4) None of these

Options

A. 61
B. 60
C. Data Inadequate
D. None of these

Answer

B

Explanation

Let Kalika.s rank from the left end =x, Ashish.s rank from the left end =y. Then, Number of students to the left of Bhupendra= `x^(3)`. Number of students to the right of Bhupendra= `y^(2)`. According to the question `x^(3)= y^(2)`, [ `because` Bhupendra is exactly midway in the row] Possible values of (x,y)= (1,1) and (4,8) only [`because` number of students in the row is less than 1000]. But, (x,y)= (1,1) is discarded or Rejected. So, Kalika.s rank from the left end `=4^(th)`. and Ashish.s rank from the left end `=8^(th)`.

So, total number of students between Kalika and Bhupendra `=(64-4)= 60`.