Question
"A boat takes 60 seconds to travel ______ metres
downstream and 40 seconds to travel ______ metres upstream in the same river. The speed of the stream is ______ m/s. Which of the following options will correctly fill the blanks in the same order to make the statement true?" I. 1440, 720, and 3 II. 1500, 600, and 5 III. 1200, 560, and 4Solution
ATQ, Let speed of boat in still water and speed of stream be, 'b' m/s and 's' m/s, respectively. For statement-I: Downstream speed of boat = b + s = (1440/60) So, b + s = 24 .... (i) Upstream speed of boat = b - s = (720/40) So, b - s = 18 .... (ii) Subtract equation (ii) from equation (i) , we get, b + s - b + s = 24 - 18 Or, 2s = 6 So, s = (6/2) = 3 Speed of stream = s = 3 m/s So, data given in statement-I is true. For statement-II: Downstream speed of boat = b + s = (1500/60) So, b + s = 25 .... (i) Upstream speed of boat = b - s = (600/40) So, b - s = 15 .... (ii) Subtract equation (ii) from equation (i), we get, b + s - b + s = 25 - 15 Or, 2s = 10 So, s = (10/2) = 5 Speed of stream = s = 5 m/s So, data given in statement-II is true. For statement-III: Downstream speed of boat = b + s = (1200/60) So, b + s = 20 .... (i) Upstream speed of boat = b - s = (560/40) So, b - s = 14 .... (ii) Subtract equation (ii) from equation (i) , we get, b + s - b + s = 20 - 14 Or, 2s = 6 So, s = (6/2) = 3 Speed of stream = s = 3 m/s ≠ 4 m/s So, data given in statement-III is false. Therefore, data given in both statement-I and statement-II is false
Sides of a parallelogram are in the ratio 7:5. Its area is 735 sq. units. Altitude on the greater side is 35 units. Altitude on the smaller side is:
The area of a square is 38 sq. cm more than the area of a rectangle of length 19 cm and breadth 17 cm. What will be the area of incircle of the square?
Suppose the ratio of the radius to the height of a cylinder is 2:3, then what is the volume of the cylinder when the total surface area of the cylinder ...
A right circular cone has a height of 24 cm and a base radius of 9 cm. What is the total surface area of the cone, including the base?
The cost of fencing a rectangular field at the rate of Rs. 6/metre is Rs. 360. If the length of the field is 11 metres more than its breadth, then find ...
The population of a town is 64000. It increased by 10% during the first year. During the second year, it decreased by 25% and increased by 5% during the...
Radius of a cylindrical vessel is 3cm less than breadth of rectangle, while height of cylindrical vessel is equal to length of rectangle, whose area is...
Mr. Arun rows a boat with the stream at 10 km/hr and against the stream in 5 km/hr. In still water, his rate of rowing in km/h is:
A cylindrical tank has a height of 10 meters and a radius of 7 meters. What is the volume of the tank?
Find how many cubes of side 1 cm each can be made by melting a cuboid with dimensions 20cm × 40cm × 5cm?