Question
Quantity I: Boat 'P' travels
540 m downstream in 45 seconds, while boat 'Q' travels 240 m upstream in 48 seconds. If the ratio of the speed of boat P in still water to the speed of boat Q in still water is 19:15, find the time it takes for boat 'P' to cover 224 m upstream. Quantity II: In a mixture of juice and water, the amount of juice exceeds the amount of water by 6 liters. The ratio of the cost of pure juice to the cost of the mixture is 5:3. If 5 liters of the mixture is replaced with the same quantity of juice, what will be the new cost of the mixture? In the question, two quantities I and II are given. You have to solve both the quantities to establish the correct relation between Quantity-I and Quantity-II and choose the correct option.Solution
ATQ, Quantity I: Let the speeds of boats P and Q in still water are ‘19x’ m/s and ‘15x’ m/s respectively. Also let the speed of the stream is ‘y’ m/s. So, 19x+y= 540/45 19x + y = 12 ---------- (1) And 15x-y= 240/48 15x – y = 5 ---------- (2) From equations (1) and (2): x = 0.5, y = 2.5 Since, the upstream speed of boat P = 19 × 0.5 – 2.5 = 7 m/s So, the time, in which boat P can cover 224 m upstream = 224/7 = 32 seconds Quantity II: Let the initial quantity of water = ‘x’ L So, the initial quantity of juice = (x + 6) L Let the cost of pure juice is Rs.’5y’ per L and the initial cost of the mixture is Rs.‘3y’ per L. So, ((x+6)×5y)/(2x+6)=3y 5x + 30 = 6x + 18 x = 12 The initial quantity of water = 12 L The initial quantity of water = 12 L The initial quantity of juice = 12 + 6 = 18 L After replacing 5 L quantity of the mixture with the same quantity of juice: The new quantity of juice = 18 – 3 + 5 = 20 L The new quantity of water = 12 – 2 = 10 L Since, we don’t know the cost of the pure juice. So, the cost of new mixture can’t be determined. Hence, relation can’t be established
The circumference of a circle is given as 220 m. What is the area of the circle? [Use π = 22/7]
A rectangular ground is 95 metre long and 75 metre broad. If two 10 metre wide paths one parallel to the breadth and one parallel to the length, of the�...
Calculate the perimeter of a rectangle, given that a circle with an area of 308 cm² has a radius that matches the diagonal of a square. The ratio betwe...
A rectangular tank measuring 10 m in length, 8 m in width, and 6 m in height is half-filled with water. Find the volume of water in the tank in liters.
Find the area of the largest circle that can be drawn in a square of side 28 cm.
The cost of fencing a square plot @ Rs.30/m is Rs. 2520. What will be the cost of flooring the plot @ Rs. 3/ square m?
- A regular tetrahedron has a lateral surface area of 108√3 cm². Calculate its volume.
The perimeter of a square field is 18 cm more than the perimeter of a rectangle. The length of the rectangle is 77 cm which is 350% of its width. If a s...
The perimeter of semicircle is 36 cm and the radius of the semicircle is equal to the height of a Cylinder whose volume is 198 cm 3 . then fi...
Rahul spends some part of his income and saves the remaining part. The ratio of his expenditure and saving is 3 : 4 respectively. If Rahul’s income i...
Relevant for Exams:
