IITJEE Foundation Maths: Tutorial Problems II

1. A, B, C start from the same place at the rates a, $a+b$, $a+2b$ kilometres per hour respectively. B starts n hours after A, how long after B must C start in order that they may overtake A at the same instant, and how far will they then have walked?
2. Find the distance between two towns when by increasing the speed 7 kilometres per hour a train can perform the journey in 1 hour less, and by reducing the speed 5 kilometres per hour can perform the journey in 1 hour more.
3. A person buys a certain quantity of land. If he had bought 7 hectares more each hectare would have cost Rs 80 less; and if each hectare had cost Rs. 360 more, he would have obtained 15 hectares less, how much did he pay for the land?
4. A can walk half a kilometre per hour faster than B; and three quarters of a kilometre per hour faster than C. To walk a certain distance C takes three-quarters of an hour more than B, and two hours more than A; find their rates of walking per hour.
5. A person spends Rs. 15 in buying goods; if each kg had cost 25 paise more he would have got 5 kg less, but if each kg had cost 15 paise less, he would have received 5 kg more; what weight did he buy?
6. Five silver coins weight 125 gm and are worth Rs. 6. Ten bronze coins weigh 500 gm and are worth 80 paise. A number of silver and bronze coins which are worth Rs. 134 weigh 11 kg and 250 gm. How many coins of each kind are there?
7. A and B are playing for money; in the first game, A loses one half of his money, but in the second he wins one-quarter of what B then has. When they cease playing, A has won Rs. 6 and B has still Rs. 14.50 more than A; with what amounts did they begin?
8. A, B, C each spend the same amount in buying different qualities of the same commodity. B pays 36 paise per kg less than A and obtains 750 gm more; C pays 60 paise per kg more than A and obtains one kg less; how much does each spend?

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