Note: The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i,e at 12 o, clock). :. The hands coincide 22 times in a day.

Note: In 12 hours the hand coincide or are in opposite direction 22 times. :. In 24 hours the hands coincide or are in opposite direction 44 times a day.

Note: In 12 hours they are at right angles 22 times. :. In 24 hours they are at right angles 44 times

Note: The hands of a clock point towards each other 11 times in every 12 hours (Because between 5 and they point towards each other at 6 0'clock only). So, in a day the hands points towards each other 22 times.

Note: At 5 o'clock, the minute hand is 25 min.spaces apart. To be coincident, it must gain 25 min.spaces. 55 min are gained in 60 min 25 min are gained in` (60/55 xx 25)` min `= 27 3/11` min

Note: To be together between 9 and 10 o'clock, the minute hand has to gain 45 min.spaces. 55 min.spaces gained in 60 min. 45 min.spaces are gained in` (60/55 xx 45)` min or `49 1/11` :. The hands are together at` 49 1/11` min.past 9.

Note: At 4 o'clock, the hands of the watch are 20 min.spaces apart. To be in opposite directions they must be 30 min. spaces apart :. Minute hand will have to gain 50 min. spaces. 55 min. spaces are gained in 60 min. 50 min. spaces are gained in` (60/55 xx 50)` min. or` 54 6/11` min. :. Required time` = 54 6/11` min. past 4.

Note: Not available

Note: Not available

Note: For an income of Rs. 12, stock needed = Rs. 100 For an income of Rs. 1200, stock needed `= Rs. (100/12 xx 1200)` `= Rs. 10000.