A 6 × 6 grid is cut from an 8 × 8 chessboard. In how many ways can we put two identical coins, one on the black square and one on a white square on the grid, such that they are not placed in the same row or in the same column?
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Jane travelled \(\frac{4}{7}\) as many miles on foot as by water and \(\frac{2}{5}\) as many miles on horseback as by water. If she covered a total of 3036 miles, how many miles did she travel on foot?
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A 75 metres long train is moving at 20 kmph. It will cross a man standing on the platform in :
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3
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A and B run a kilometre and A wins by 25 sec. A and C run a kilometre and A wins by 275 m. When B and C run the same distance, B wins by 30 sec. The time taken by A to run a kilometre is :
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4
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The average speed of a train is 20% less on the return journey than on onward journey. The train halts for half an hour at the destination station before starting on the return journey. If the total time taken for the to and fro journey is 23 hours, covering a distance of 1000 km, the speed of the train on the return journey is:
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5
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Page and Plant are running on a track AB of length 10 metres. They start running simultaneously from the ends A and B respectively. The moment they reach either of the ends, they turn around and continue running. Page and Plant run with constant speeds of 2m/s and 5m/s respectively. How far from A (in metres) are they, when they meet for the 23rd time?
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A can give 40 metres start to B and 70 metres to C in a race of one kilometre how many metres starts can B give to C in a race of one kilometre ?
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7
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Amit travelled black to home in a car, after visiting his friend in a distant village. When he stated at his friend's house the car had exactly 18 litres of petrol in it. He travelled along at a steady 40 kilometres per hour and managed a 10 kilometres per litre of petrol. As the car was old, the fuel tank lost fuel at the rate of half a litre per hour. Amit was lucky as his car stopped just in front of his home because it had rum out of fuel and he only just made it. How far was it from his friend's home to Amit's home ?
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The speeds of three cars are the ratio 2 : 3 : 4. The ratio of the taken by these cars to travel the same distance is :
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A thief seeing a policeman at a distance of 150 metres starts running at 10 kmph and the policeman gives immediate chase at 12 kmph. When the thief is overtaken the thief has traveled a distance of:
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10
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A boat covers 48 km upstream and 72 km downstream in 12 hours, while it covers 72 km upstream and 48 km downstream in 13 hours The speed of stream is :
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