39

Initial Amount = Rs. 153,300

Repeating same steps:

Amount left after Temple 2: Rs. 38,100
Amount left after Temple 3: Rs. 18,900
Amount left after Temple 4: Rs. 9,300
Amount left after Temple 5: Rs. 4,500
Amount left after Temple 6: Rs. 2,100
Amount left after Temple 7: Rs. 900
Amount left after Temple 8: Rs. 300
Amount left after Temple 9: Rs. 0.

48

The second one will NOT be a triangle. For a triangle, the sum of lengths of any two sides must be more than the length of the third. Put differently, the area of the (imaginary) “triangle” will be ZERO,  whereas the first triangle, however small it may be, will have a bigger area.

Assumption: The ‘mps‘ in the ’40 mps’ stands for metres per second (rather than miles per second, which is impossible on a bike)

Ans: 118.325 miles

49.162 miles at 55mph and  69.162 miles at 40mps (~ 89.497 miles per hour)

Time taken for the first 49.162 miles at 55mph = 0.894 Hrs
Time for next 69.162 miles at 89.497 mph = 0.773 Hrs.

Total time travelled = 1.667 hrs ~ 100 min

110

(72927 + 110 = 73037)

24

Assuming that our hypothetical bank accepts amounts rounded off to two decimal places, the nearest possible initial amount must be Rs. 63.98. Starting with this amount, by the end of 6th year, the balance will be –0.28 (effectively zero).  (If started with Rs. 63.99, the final balance would be Rs. 0.36 (which is more than 0.)

Arrange them in a pyramid formation, with three balls touching each other forming a triangular base and the fourth one sitting on top of the base. (See image)