In order that the little girl should have disposed of the oranges she had remaining after her second  sale, she; must have had at least one whole orange remaining so that she could deduct from it ‘half of her oranges plus half an orange’, for the third and the final sale. Therefore, if 1 orange represents half of the remaining after the second sale, then she must have sold two oranges in her second sale, leaving the 3 oranges after the first sale.
Lastly if three oranges only represent half the original number, plus half an orange, then she must have started with [ (3×2)+1] or 7 oranges.

While striking 7 the clock strikes its first gong at 7 o’clock and it strikes 6 more at regular intervals. These 6 intervals take 7 seconds so that the intervals between gongs is 7/6  seconds. However to
strike 10 there are 9 intervals each taking 7/6×9 seconds for a total of 10.5 seconds.

The Police Officer took thirty steps. In the same time’ the thief took forty-eight, which added to his start of twenty-seven, carried fiim seventy-five steps. This distance would be exactly equal to thirty steps of the Police Officer.

Here is the formula that gives the minutes past twelve to which the hour hand points when the minute hand is exactly thirty minutes ahead.
Minutes past twelve Y=30/11[ (n—1) 2+1] where n is the next hour— Let’s take the case of at what time between 4 and 5 will the hands be opposite each other? (n= 5).
Y=30/11 x9 =270/11 . i.e. the hour hand will be 270/11  minutes past 4. The formula may be derived from the following: If X is distance moved by the minute hand Y is the distance moved by hour hand
then X—Y = 30 First time the hands move round X = 12 Y Second time the hands move round X = 12 Y—5 Third time the hands move round X = 12 Y—10

By experiment’we find that the only numbers that can be turned upside down and still read as a number are 0, 1, 6, 8 and 9.
The numbers 0, 1 and 8 remain 0, 1 and 8 when turned over, but 6 becomes 9 and 9 becomes 6. Therefore the possible numbers on the bus were 9, 16, 81, 100, 169 or 196. However, the number 196 is the only number which becomes a perfect square when turned over because 961 is the perfect square of 31. Therefore 196 is the correct answer.

The lowest square number I can think of, contain-ing all the nine digits once and only once, is 139854276, the square of 11826, and the highest square number under the. same conditions is 932187456 the square of 30384

One’can think of different answers for this question, but yet the correct answer is very simple. All we have to consider is that the shopowner could not have possibly lost more than the tourist actually stole.
The tourist got away with the bicycle which cost the shopowner Rs. 300 and the Rs. 50 ‘change’, and therefore he made off with Rs. 350. And this is the exact amount of the shopkeeper’s loss.

C continues to fly alongside A until they are 1/4 of the distance around the world. At this point C completely fills the tank of A which is now able to fly to a point 3/4 of the way around the world. C has now only 1/3 of its full fuel capacity left, not enough to get back to the home base. But the first ‘auxiliary’ aircraft reaches it in time in order to refuel it, and both ‘auxiliary’ aircraft are the able to return safely to the home base.

Now in the same manner as before both B and C fully refuelled fly towards A. Again B refuels C and returns home to be refuelled. C reaches A at the point where it has flown 3/4 around the world. All 3 aircraft can safely return to the home base, if the refuelling process is applied analogously as for the first phase of the flight.

The series lists numbers that are flanked by two prime numbers.

4 (3 and 5 are prime)
6 (5 and 7 are prime)
12 (11 and 13 are prime)
18 (17 and 19 are prime)
30 (29 and 31 are prime)
42 (41 and 43 are prime)
60 (59 and 61 are prime)
72 (71 and 73 are prime)
102 (101 and 103 are prime)
108 (107 and 109 are prime)

thus

138 (137 and 139 are prime), 150 (149 and 151 are prime), 180 (179 and 181 are prime)

For this answer is 3^0, 3^1, 3^2… That is 1,3,9,27,81,243 and 729