Sunday Coffee Time Puzzles !

1. A train, an hour after starting, meets with an accident which detains it an hour, after which it proceeds at three-fifths of its former rate and arrives 3 hours after time; but, had the accident happened 50 miles further on the line, it would have arrived 1.5 hours sooner: find the length of the journey.
2. A body of men were formed into a hollow square, three deep, when it was observed, that with the addition of 25 to  their number a solid square might be formed, of which the number of men in each side would be greater by 22 than the square root of the number of men in each aide of the hollow square: required the number of men.
3. A set out to walk at the rate of 4 miles an hour; after he had been walking $2\frac{3}{4}$, B set out to overtake him and went $4\frac{1}{2}$ miles the first hour, $4\frac{3}{4}$ miles the second, 5 the third, and so gaining a quarter of a mile every hour. In how many hours would he overtake A?
4. A man wishing his two daughters to receive equal portions when they came of age bequeathed to the elder the accumulated interest of a certain sum of money invested at the time of his death in 4 per cent stock at 88; and to  the younger he bequeathed the accumulated interest of a sum less than the former by $\pounds 3500$ invested at the same time in the 3 per cents, at 63. Supposing their ages at the time of their father’s death to have been 17 and 14, what was the sum invested in each case, and what was each daughter’s fortune?
5. A and B travelled on the same road and at the same rate from Huntington to London. At the $50^{th}$ milestone from London, A overtook a drove of geese which were proceeding at the rate of 3 miles in 2 hours; and two hours afterwards met a waggon, which was moving at the $46^{th}$ milestone, and met the waggon exactly 40 minutes before he came to the $31^{st}$ milestone. Where was B when A reached London?
6. To complete a certain work, a workman A alone would take m times as many days as B and C working together; B alone would take a times as many days as A and C together; C alone would take p times as many days as A and B together; show that the numbers of days in which each would do it alone are as $m+1:n+1:p+1$.
7. A traveller set out from a certain place, and went 1 mile the first day, 3 the second, 5 the next, and so on, going every day 2 miles more than he had gone the preceding day. After he had been gone three days, a second sets out, and travels 12 miles the first day, 13 the second and so on. In how  many days, will the second overtake the first? Explain the double answer.
8. A number of persons were engaged to do a piece of work which would have occupied them 24 hours if they had commenced at the same time; but instead of doing so, they commenced at equal intervals and then continued to work till the whole was finished, the payment being proportional to the work done by each: the first comer received eleven times as much as the last; find the time occupied.
9. There are three towns A, B and C; a person by walking from A to B, driving from B to C, and riding from C to A makes the journey in 15.5 hours; by driving from A to B, riding from B to C, and walking from C to A, he could make the journey in 12 hours. On foot he could make the journey in 22 hours, oh horseback in 8.25 hours, and driving in 11 hours. To walk a mile, ride a mile, and drive a mile he takes altogether half an hour; find the rates at which he travels, and the distance between the towns.
10. In a mixed company consisting of Poles, Turks, Greeks, Germans and Italians, the Poles are one less than the one-third of the number of Germans, and three less than half the number of Italians. The Turks and Germans outnumber the Greeks and Italians by 3; the Greeks and Germans form one less than the half the company; while the  Italians and Greeks form seven-sixteenths of the company; determine the number of each nation.

More fun later,

Nalin Pithwa

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