Question
Three pipes A, B and C can fill/empty a tank. A can fill
it in 12 hours, B in 15 hours, and C can empty a full tank in 20 hours. All three pipes are opened together. After some time, pipe C is closed and A and B together fill the remaining tank in 5 hours. If the tank is exactly full at the end, for how many hours was pipe C kept open?Solution
ATQ, Filling rates: A = 1/12, B = 1/15, C (emptying) = −1/20 (per hour). A + B = 1/12 + 1/15 = (5 + 4)/60 = 9/60 = 3/20. A + B + C = 3/20 − 1/20 = 2/20 = 1/10. Let C be open for x hours (all three working). Volume filled in this time = x × (1/10) = x/10. After C is closed, A + B work for 5 hours: Volume filled = 5 × (3/20) = 15/20 = 3/4. Total volume = 1 ⇒ x/10 + 3/4 = 1 ⇒ x/10 = 1 − 3/4 = 1/4 ⇒ x = 2.5 hours.
∆ABC and ∆DEF are similar and their areas are respectively 16 cm2 and 64 cm 2 . If EF = 6 cm BC is?
O is the circum centre of the isosceles ∆ ABC. Given that AB = AC = 5 cm and BC = 6 cm. The radius of the circle is
Find the ratio between the area of the in-circle and the circum-circle of a square?
AB is parallel to DC in a trapezium ABCD. It is given that AB > DC and the diagonals AC and BD intersect at O. If AO=3x-15, OB = x +9, OC =x-5 and OD = ...
In the given figure, AB, AE, EF, FG and GB are semicircles. AB = 56 cm and AE = EF = FG = GB. What is the area (in cm2) of the shaded region?...
The ratio of the angles ∠A and ∠B of a non-square rhombus ABCD is 7:5, then the value of the ∠C is
The cost of diamond varies directly as the square of its weight. A diamond broke into four pieces with weights in the ratio 1: 4: 5: 6. if the loss in t...
A triangular field has sides 13 m, 14 m, and 15 m. A well with a diameter of 7 m is dug outside the field. If the entire soil dug from the well is used ...
Determine the difference between an angle and its complementary angle, given that the angle is two-thirds of its complement.
