Two water taps together can fill a tank in  hours. The tap of

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 Multiple Choice QuestionsLong Answer Type

31. In a class, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product would have been 210. Find her marks in the two subjects.
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32. The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.
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33. The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.
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34. A train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, would have taken 1 hour less for the same journey. Find the speed of the train.
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35. Two water taps together can fill a tank in space 9 3 over 8 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.


Suppose the time taken by the larger tap to fill the tank is x hours.
∴     Time taken by the smaller tap to fill the tank = (x + 10) hours
 Now, Portion of the tank filled by the larger tank  in 1 hour = 1 over straight x
Portion of the tank filled by the smaller tank in 1 hour = fraction numerator 1 over denominator straight x plus 10 end fraction and Portion of the tank filled by the both in 1 hour
equals 1 over straight x plus fraction numerator 1 over denominator straight x plus 10 end fraction equals fraction numerator straight x plus 10 plus straight x over denominator straight x left parenthesis straight x plus 10 right parenthesis end fraction
equals space fraction numerator 2 straight x plus 10 over denominator straight x left parenthesis straight x plus 10 right parenthesis end fraction equals fraction numerator 2 left parenthesis straight x plus 5 right parenthesis over denominator straight x left parenthesis straight x plus 10 right parenthesis end fraction space space space... left parenthesis straight i right parenthesis
It is given that,
Portion of the tank filled by both in 1 hour  = 8 over 75
                                                                     ..(ii)
∴   From (i) and (ii), we get
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rightwards double arrow space space space space space space space space space space space space space space space space space space space fraction numerator straight x plus 5 over denominator straight x squared plus 10 straight x end fraction equals 4 over 75
rightwards double arrow space space space space space space space space space space space space space space space space space space space space space 75 straight x plus 375 space equals space 4 straight x squared plus 40 straight x
rightwards double arrow space space space space space 4 straight x squared plus 40 straight x minus 75 straight x minus 375 space equals space 0
rightwards double arrow space space space space space space space space space space space space space space space 4 straight x squared minus 35 straight x minus 375 space equals space 0
space therefore space space space space space space space space space space space straight x space equals space fraction numerator 35 plus-or-minus square root of left parenthesis 35 right parenthesis squared minus 4 cross times 4 cross times left parenthesis negative 375 right parenthesis end root over denominator 2 cross times 4 end fraction
space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 35 plus-or-minus square root of 1225 plus 6000 end root over denominator 8 end fraction
space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 35 plus-or-minus square root of 7225 over denominator 8 end fraction equals fraction numerator 35 plus-or-minus 85 over denominator 8 end fraction
                     
                  equals fraction numerator 35 plus 85 over denominator 8 end fraction space or space fraction numerator 35 minus 85 over denominator 8 end fraction

                   equals space 120 over 8 space or space fraction numerator negative 50 over denominator 8 end fraction

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#6 {main}</pre>              space space open square brackets fraction numerator negative 50 over denominator 8 end fraction space is space rejected close square brackets
Hence, Time taken by the larger tap = 15 hrs and time taken by the smaller tap = (15 +10) = 25 hrs.
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36. An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11 km/hr more than that of the passenger train, find the average speed of the two trains.
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37. Sum of the area of the two squares is 468 m2. If the difference of their perimeters is 24 m, find the sides of the two squares.
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 Multiple Choice QuestionsShort Answer Type

38. Find the discriminant of the following quadratic equations. If the real roots exist, find them
2 straight x squared minus 3 straight x plus 5 space equals space 0
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 Multiple Choice QuestionsLong Answer Type

39. Find the discriminant of the following quadratic equations. If the real roots exist, find them
3 straight x squared minus 4 square root of 3 straight x plus 4 equals 0

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 Multiple Choice QuestionsShort Answer Type

40. Find the discriminant(or the nature of the roots) of the following quadratic equations. If the real roots exist, find them
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#6 {main}</pre>


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