Answer :
Let, the time taken by smaller tap to fill the tank completely = x
hours
The volume of the tank filled by a smaller tap in 1 hour =
The time taken by larger tap to fill the tank completely = x - 2
hours
The volume of the tank filled by a larger tap in 1 hour
Time taken by the tank to fill hours
hours
The volume of the tank filled by a smaller tap in hours
The volume of the tank filled by a larger tap in hours
⇒ 15(x - 2) + 15x = 8x(x-2)
⇒15(x – 2 + x) = 8x(x – 2)
⇒ 15(2x - 2) = 8x2 - 16
⇒8x2 – 46x + 30 = 0
⇒2(4x2 – 23x + 15) = 0
⇒4x2 – 23x + 15 = 0
⇒4x2 – 20x - 3x + 15 = 0
⇒ 4x(x -5) - 3(x - 5) = 0
⇒ (4x-3) (x -5) = 0
At x = 5
Time taken by smaller tap to fill the tank completely = 5 hours
Time taken by larger tap to fill tank completely = 5 – 2 = 3 hours
At
Time taken by smaller tap to fill the tank completely hours
Time taken by larger tap to fill the tank completely
hours
Time is not possible to be negative.
So, is not possible.
OR
Let, speed of the stream = x km/h
And the speed of the boat = y km/h
So, the speed of the upstream = (y – x) km/h
And the speed of the downstream = (y + x) km/h
…(1)
…(2)
Let,
The equations will be:
30u + 44v - 10 = 0
40u + 55v - 13 = 0
By cross multiplication method we know,
Here a1 = 30 , b1 = 44 , c1 = -10
a2= 40, b2 = 55, c2 = -13
So,
Now,
⇒ 10 = 2(y - x)
⇒ 10 = 2y - 2x
⇒ 5 = y - x .... (3)
⇒ 5 + x = y
And
⇒ y + x = 11 ..... (4)
Put the value of y in eq (4),
⇒ 5 + x + x = 11
⇒ 5 + 2x = 11
⇒2x = 6
⇒ x = 3
Put the value of x in (3) to get,
⇒ 5 = y - 3
⇒ y = 8
So, speed of the stream = 3 km/h
And the speed of the boat = 8 km/h
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