A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of stream

 A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of stream

x=speed of the stream in km/hr 

speed of boat upstream =(18-x)km/hr

speed of the boat downstrream=(18+x)km/hr

distance=24km

time=distance/speed

t1=24/(18-x)hours upstream

t2=24/(18+x) hours downstream

given t1=t2  + 1

t1 - t2=1

[24 / (18-x)]-[24/(18+x)]=1

48x/[324-(x"2)]=1

(x"2)+48x-324=0

[x-6][x+54]=0

x=6 or x= -54 [reject]

speed of stream =6 km/hr

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 questions in old cbse sample question papers for 10th  mathematics

  National Art convention got registrations from students from all parts of the country, of which 60 are interested in music, 84 are interested in dance and 108 students are interested in handicrafts. For optimum cultural exchange, organisers wish to keep them in minimum number of groups such that each group consists of students interested in the same art form and the number of students in each group is the same. Find the number of students in each group. Find the number of groups in each art form. How many rooms are required if each group will be allotted a room

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A had some chocolates, and he divided them into two lots A and B. He sold the first
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Find the total number of chocolates he had.

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n the given figure, arcs have been drawn of radius 7cm each with vertices A, B, C
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(i) At least one head?
(ii) At most one tail?
(iii) A head and a tail?

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The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.
(i) If the first circular row has 30 seats, how many seats will be there in the 10th row?
(ii) For 1500 seats in the auditorium, how many rows need to be there?

If 1500 seats are to be arranged in the auditorium, how many seats are still left to
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(iii) If there were 17 rows in the auditorium, how many seats will be there in the
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solution

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radius 2.8 m and height 3.5 m and the upper part is conical with the same base
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