1.spinning 3 hours daily,kanika can spin 2kg cotton-balls in 12 days.spinning 4hours daily how many days will she take to spin 10 kg cotton balls?
1.45 days
2.42 days
3.38 days
4.none of these
2.a train travels at a certain average speed for a distance of 63 km.there after it travels a distance of 72 km with an average speed of a 6 km/hr more than the original speed.total time taken to complete the journey is 3hours.what is the original average speed of the train?
1.36km/hr 2.42km/hr 3.48km/hr 4.none of these
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We know that ,
( H1 × D1 )/k1 = ( H2 × D2 )/K2
( 3 × 12 )/2 = ( 4 × x )/10
( 3 × 12 × 10 )/( 2 × 4 ) = x
after cancellation , we get
45 = x
Therefore ,
Number of days = D2 = 45
*************************************
2 ) Let the Original average speed of
the train ( s1 ) = x km/hr
distance travelled ( d1 ) = 63 km
time ( t1 ) = d1/s1
t1 = 63/x hr ---( 1 )
3 ) If speed of the train increased,
new speed ( S2 ) = ( x + 6 )km/hr
distance ( d2 ) = 72 km
time ( t2 ) = d2/s2
t2 = 72/( x + 6 ) ---( 2 )
according to the problem given ,
t1 + t2 = 3 hours
63/x + 72/( x + 6 ) = 3
divide each term with 6 , we get
21/x + 24/( x + 6 ) = 1
[ 21( x + 6 ) + 24x ]/[ x( x + 6 ) ] = 1
21x + 126 + 24x = x² + 6x
126 + 45x = x² + 6x
0 = x² + 6x - 45x - 126
x² - 39x - 126 = 0
x² - 42x + 3x - 126 = 0
x( x - 42 ) + 3( x - 42 ) = 0
( x - 42 )( x + 3 ) = 0
x - 42 = 0 or x + 3 = 0
x = 42 or x = -3
but x should not be negative.
Therefore ,
Original average speed of the
train = x = 42km/hr
I hope this helps you.
: )
( H1 × D1 )/k1 = ( H2 × D2 )/K2
( 3 × 12 )/2 = ( 4 × x )/10
( 3 × 12 × 10 )/( 2 × 4 ) = x
after cancellation , we get
45 = x
Therefore ,
Number of days = D2 = 45
*************************************
2 ) Let the Original average speed of
the train ( s1 ) = x km/hr
distance travelled ( d1 ) = 63 km
time ( t1 ) = d1/s1
t1 = 63/x hr ---( 1 )
3 ) If speed of the train increased,
new speed ( S2 ) = ( x + 6 )km/hr
distance ( d2 ) = 72 km
time ( t2 ) = d2/s2
t2 = 72/( x + 6 ) ---( 2 )
according to the problem given ,
t1 + t2 = 3 hours
63/x + 72/( x + 6 ) = 3
divide each term with 6 , we get
21/x + 24/( x + 6 ) = 1
[ 21( x + 6 ) + 24x ]/[ x( x + 6 ) ] = 1
21x + 126 + 24x = x² + 6x
126 + 45x = x² + 6x
0 = x² + 6x - 45x - 126
x² - 39x - 126 = 0
x² - 42x + 3x - 126 = 0
x( x - 42 ) + 3( x - 42 ) = 0
( x - 42 )( x + 3 ) = 0
x - 42 = 0 or x + 3 = 0
x = 42 or x = -3
but x should not be negative.
Therefore ,
Original average speed of the
train = x = 42km/hr
I hope this helps you.
: )
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