Anjali’s Rides:
Anjali took Ride-1 at 11 am after waiting 30 minutes (i.e., from 10:30 am).
It was the only ride where Anjali waited, meaning she started other rides immediately when the gates opened.
Cost Details:
By 12:15 pm, Anjali and Bipasha each spent Rs. 50.
Last Ride Information:
The last ride taken by Anjali and Bipasha was the same (Ride-4).
Bipasha waited 30 minutes for Anjali to finish this ride.
Bipasha took a 1-hour coffee break before queuing for Ride-4.
Additional Ride Needed:
Total spent so far: Rs. 20 + Rs. 30 + Rs. 40 = Rs. 90
Remaining to reach Rs. 140: Rs. 50
So Anjali must have taken Ride-2 (Rs. 50).
Final Summary:
Anjali’s rides:
Total Cost = \( 20 + 30 + 40 + 50 = \mathbf{140} \) rupees.
A train travels from Station A to Station E, passing through stations B, C, and D, in that order. The train has a seating capacity of 200. A ticket may be booked from any station to any other station ahead on the route, but not to any earlier station. A ticket from one station to another reserves one seat on every intermediate segment of the route. For example, a ticket from B to E reserves a seat in the intermediate segments B– C, C– D, and D–E. The occupancy factor for a segment is the total number of seats reserved in the segment as a percentage of the seating capacity. The total number of seats reserved for any segment cannot exceed 200. The following information is known. 1. Segment C– D had an occupancy factor of 952. Exactly 40 tickets were booked from B to C and 30 tickets were booked from B to E. 3. Among the seats reserved on segment D– E, exactly four-sevenths were from stations before C. 4. The number of tickets booked from A to C was equal to that booked from A to E, and it was higher than that from B to E. 5. No tickets were booked from A to B, from B to D and from D to E. 6. The number of tickets booked for any segment was a multiple of 10.
For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is: