LAST TIME REVISION RATIO AND PROPORTION (3)

1) If A: B=3:4 and B: C= 6:7, find:
a) A: C.
b) A: B: C.

2) If P: Q=9:4 and P:R= 6:11, find:
a) Q: R.
b) P: Q: R

3) Share out 120 hours of computer time between 4 scientists in the ratio 2:1:4:3.

4) The population of three villages are 2500, 3750 and 7500. A consignment of 13200 tonnes of grain is to be shared according to the population. How much goes to each village ?

5) Increase Rs450 in the ratio 5:2.
6) Decrease 7.20 kg in the ratio 7:11.

7) Divide Rs6902 among A, B and C so that A's share is to B's share as 1:2 and B's share is to be  3:4.

8) Divide 3900 among A, B and C so that the four times A's share, three times B's share and twice C's share may all be equal.

9) Find : i) the four proportion to 6, 7 and 9.
ii) the third proportional to 2.4 and 0.72.
ii) the mean proportional to 8 and 18.

10) Two numbers are in the ratio 5:4. When 30 is subtracted from each, the resulting numbers have the ratio 4:3. Find the numbers.       

11) A garrison of 3000 men has provisions for 64 days. At the end 24 days, reinforcement arrives and it is found that now the remaining provisions will last 24 days only. What is the strength of reinforcement.

12) A man undertakes to do a certain work in 150 days. He employees 200 men. He finds that only a quarter of the work is done in 50 days .  How many additional men should he employ so that the whole work is finished in time ?

13) A garrison of 3600 men was provisions for 15 weeks. How long will the provisions last, if 900 more men join them and the daily allowance per man is reduced by 20%?

14) If 50 men can do a piece of work in 12 days working 8 hours a day, how many hours a day would 60 men have to work in order to do another piece of work, twice as big in 16 days ?

15)  Two men undertakes to do a piece of work for Rs288. One can do it in 8 days and the other in 9 days; but with the help of a boy they finish the work in 7/2 days. Find the share of each in the money.

16) A car travelling at 90 kmph completes a certain journey in 40 minutes. How long would it take a car travelling at 
a) 100 kmph
b) 75 kmph to complete the same journey?

17) Water flows constantly into a cylindrical beaker with a base area 24 cm². The water level rises by 10cm every second. How quickly would the water level rise in a beaker with a base area of
a) 20 cm²
b) 30 cm², if the flow rate remains the same.

18) A 1.2 kilowatt electric heater boils a given amount of water in 10 minutes. How long would it take
a) a less powerful heater of 800 watts.
b) a more powerful heater of 2 kilowatt to boil the same amount of water?

19) A man walks from his house at 5 km an hour and reaches his office 20 minutes late. If his speed had been 15/2 kmph, he would have reached 12 minutes early. How far his office from his house ?

20) A man sitting in a train, which is travelling at the rate of 50 kmph, observes that it takes 6 seconds for a good train, travelling in the opposite direction, to pass him. If the goods train is to 220 m long, its speed.

21) A train overtakes two person who are walking in the same direction at 2 kmph and 4 kmph respectively and passes them in 9 seconds and 10 seconds respectively. Find the length of the train and its speed in kmph .

22) A railway train crosses a platform 110m long in 10 seconds and passes a telegraph post in 5 seconds . Find the length of the train and its speed per hour.

23) A boat moves down 0-steam at the rate of 1 km in 6 minutes and upstream at the rate of 6 kmph. What is the velocity of the current ?

24) The current of a stream runs at the rate of 5 kmph . A motor-boat goes 10 km upstream and back again to its starting point in 50 minutes. Find the speed of the motor boat in still water.

25) Find two numbers in the ratio of 5 to 4 so that the difference of their cubes is 488.

26) A certain number of labourers promise to do a certain piece of work in 10 days, but 5 of them become absent. If the rest of the labourers complete the work in 12 days, find their original number.

27) A man can walk 600 km in 35 days, resting 9 hours each day; how long will he take to walk 375 km if he rests 10 hours each day and walks 3/2 times as fast as before?

28) How many one rupees coins , fifty paise coins and twenty -five paise coins, of which the numbers are proportional to 4, 5 and 6, are together worth Rs96 ?

29) If 3 men or 4 women can reap a field in 43 days; how long will 7 men and 5 women take to reap it ?

30) Two pipes  P and Q can fill a cistern in 12 minutes and 15 minutes respectively. Both are opened together, but at the end of 3 minute the first is turned off . In how much time will the remaining cistern be filled?

31) Two men A and B walk from P to Q (a distance of 21 km) at 3 kmph and 4 kmph respectively. B reaches A, returns immediately and meets A at R. Find the distance from P to R.

32) The wheel of an engine, 4 m 20 cm in circumference, makes 15 revolutions in 4 seconds ; find the speed of the engine in kmph.


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