Algebra

Progression & Series

Medium

A lift carrying 50 passengers from the ground floor of a 100-storeyed building is moving upwards. The lift stops at the 1st, 2nd, and 3rd floor, then skips the 4th floor, again stops at the 5th, 6th, and 7th, then skips the 8th floor, and so on. Passengers get discharged in a pattern. 2, 3, 3, 2, 3, 3..... On which floor does the lift become empty?

25th floor

28th floor

23rd floor

None of these

✅ Correct Option: 1

The lift stops at floors: $1, 2, 3$ , skips $4$ , then $5, 6, 7$ , skips $8$ , then $9, 10, 11$ , skips $12$ , and so on.

Pattern: Stop $3$ floors → Skip $1$ floor → Repeat

Passenger discharge pattern: $2, 3, 3, 2, 3, 3, 2, 3, 3...$ (repeats every $3$ stops)

Tracking passengers remaining after each stop:

Stop	Floor	Discharged	Remaining
Start	Ground	$0$	$50$
$1$	$1$	$2$	$48$
$2$	$2$	$3$	$45$
$3$	$3$	$3$	$42$
$4$	$5$	$2$	$40$
$5$	$6$	$3$	$37$
$6$	$7$	$3$	$34$
$7$	$9$	$2$	$32$
$8$	$10$	$3$	$29$
$9$	$11$	$3$	$26$
$10$	$13$	$2$	$24$
$11$	$14$	$3$	$21$
$12$	$15$	$3$	$18$
$13$	$17$	$2$	$16$
$14$	$18$	$3$	$13$
$15$	$19$	$3$	$10$
$16$	$21$	$2$	$8$
$17$	$22$	$3$	$5$
$18$	$23$	$3$	$2$
$19$	$25$	$2$	$0$

The lift becomes empty on floor $25$ .

BMSAT Kozhikode 2025

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BMSAT Kozhikode 2026

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Solution

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