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Shatabdi Express without its rake can go 36 km in an hour, and the speed is diminished by a quantity that varies as the square root of the number of wagons attached. If it is known that with four wagons its speed is 24 km/h, the greatest number of wagons with which the engine can just move is

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Important Questions on Ratio, Proportion and Variation

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If f(x) =x+1x-1 ,then the ratio of x to f(y) where y = f(x) is
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Sahil employs 200 men to build a bund. They finish 56 of the work in 10 weeks. Because of some natural calamity not only does the work remain suspended for 4 weeks but also half of the work already done is washed away. After the calamity, when the work is resumed, only 140 men turn up. The total time in which the contractor is able to complete the work assuming that there are no further disruptions in the schedule is
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Rahim covers a distance of 48 km performed by train, bike and car in that order, the distance cov- ered by the three ways in that order are in the ratio of 8:1:3 and charges per kilometer in that order are in the ratio of 8:1:4. If the train charges being 24 per kilometer, the total cost of the journey is
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A bag contains 25 paise, 50 paise and 1  coins. There are 220 coins in all and the total amount in the bag is 160. If there are thrice as many 1 coins as there are 25 paise coins, then what is the number of 50 paise coins?
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Read the following and answer the questions that follow. Sahir runs in a triathlon consisting of three phases in the following manner. Running 12 km, cycling 24 km and swimming 5 km. His speeds in the three phases are in the ratio 2:6:1. He completes the race in n minutes. Later, he changes his strategy so that the distances he covers in each phase are constant but his speeds are now in the ratio 3:8:1. The end result is that he completes the race taking 20 minutes more than the earlier speed. It is also known that he has not changed his running speed when he changes his strategy.

What is his initial speed while swimming?

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If his speeds are in the ratio 1:3:1, with the running time remaining unchanged, what is his finishing time?
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Read the following and answer the questions that follow. Sahir runs in a triathlon consisting of three phases in the following manner. Running 12 km, cycling 24 km and swimming 5 km. His speeds in the three phases are in the ratio 2:6:1. He completes the race in n minutes. Later, he changes his strategy so that the distances he covers in each phase are constant but his speeds are now in the ratio 3:8:1. The end result is that he completes the race taking 20 minutes more than the earlier speed. It is also known that he has not changed his running speed when he changes his strategy.

What is Sahir's original speed of running?