## IITJEE Foundation practice or training problem sheet: I

1. If the numerator of a fraction is increased by 5, it reduces to $\frac{2}{3}$, and if the denominator is increased by 9, it reduces to $\frac{1}{3}$. Find the fraction.
2. Find a fraction such that it reduces to $\frac{3}{5}$ if 7 is subtracted from its denominator, and reduces to $\frac{3}{8}$ on subtracting 3 from its numerator.
3. If unity is taken from the denominator of a fraction, it reduces to $\frac{1}{2}$; if 3 is added to the numerator it reduces to $\frac{4}{7}$, find the required fraction.
4. Find a fraction which becomes $\frac{3}{4}$ on adding 5 to the numerator and subtracting 1 from its denominator; and, reduces to $\frac{1}{3}$ on subtracting 4 from the numerator and adding 7 to the denominator.
5. If 9 is added to the numerator a certain fraction will be increased by $\frac{1}{3}$; if 6 is taken from the denominator the fraction reduces to $\frac{2}{3}$; find the required fraction.
6. At what time between 9 and 10 o’clock are the hands of a watch together?
7. When are the hands of a clock 8 minutes apart between the hours at 5 and 6 ?
8. At what time between 10 and 11 o’clock is the hour hand six minutes ahead of the minute hand?
9. At what time between 1 and 2 o’clock are the hands of a watch in the same straight line?
10. At what times between 12 and 1 o’clock are the hands of a watch at right angles?
11. A person buys 20 m of cloth and 25 m of canvas for Rs. 22.50. By selling the cloth at a gain of 15 per cent, and the canvas at a gain of 20 per cent, he clears Rs. 3.75. Find the price of each per metre.
12. A dealer spends Rs. 6950 in buying horses at Rs, 250/- each and cows at Rs. 200/- each; through disease, he loses 20 percent of the horses and 25 % of the cows. By selling the animals at the price he gave for them, he receives Rs. 5400/-. Find how many of each kind he bought.
13. The population of a certain district is 53000, of whom 835 can neither read nor write. These consists of 2 %, of all the males and 3 % of all the females; find the number of males and females.
14. Two persons C and D start simultaneously from two places a kilometre apart, and walk to meet each other; if C walks p kilometres per hour, and D one kilometre per hour faster than C, how far will D have walked when they meet?
15. A can walk a kilometres per hour faster than B; supposing that he gives B a start of c kilometres, and that B walks a kilometres per hour, how far will A have walked when he overtakes B?

Cheers,

Nalin Pithwa

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