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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Two coins are tossed simultaneously. What is the probability of getting
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(iii) A head and a tail?
To fill a swimming pool two pipes are used. If the pipe of larger diameter used for 4 hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool?
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.
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(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
be put after 10th row?
(iii) If there were 17 rows in the auditorium, how many seats will be there in the
middle row
Due to heavy floods in a state, thousands were rendered homeless. 50 schools
collectively decided to provide place and the canvas for 1500 tents and share the
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radius,
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per m^2,find the amount shared by each scho15ol to set up the tents
If tan (A + B) = √3 and tan (A – B) = 1/√3
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Find the value of x if
2 [ cosec30)^2 ] + x [(sin60)^2] – (3/4)(tan30)^2 = 10 where the angles are in degrees
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