CUET-General Aptitude-14/04/2025
Dear Students, we welcome you in our post CUET-General Aptitude-14/04/2025.
Our today’s post is on boats and streams as below:
Important Formulae:
If the speed of a boat in still water is x km/h and speed of the stream is y km/h, then
(1) Downstream Speed of boat= (𝑥+y) km/h
(2) Upstream Speed of boat= (𝑥-y) km/h
(3) Speed of boat in still water, 𝑥= (Downstream Speed+Upstream Speed)/2
(4) Speed of stream, y= (Downstream Speed-Upstream Speed)/2
Here, Still water means the speed of water of a river is zero. Stream means speed of the moving water of a river. Downstream means moving of water and boat in the same direction. Upstream means moving of water of a river and boat in opposite direction.
Q 3583) A, can go downstream thrice as fast as he can go upstream between two specific points on a river. If the river flows at 8 km/hr, what is the speed of the boat in still water? …………………(CUET UG 2024, Delhi)
(A) 12 km/h (B) 14 km/h (C) 16 km/h (D) 18 km/h
Ans: (C) 16 km/h
Solution:
Let the speed of the boat in still water is 𝑥 km/h. The speed of the stream is 8 km/h, then
Step 1st:
(1) Downstream Speed of boat= (𝑥+8) km/h
Step 2nd:
(2) Upstream Speed of boat=(𝑥-8) km/h
Step 3rd:
According to the question, Downstream Speed of boat is equal to the thrice Upstream Speed of boat.
∴ (𝑥+8) =3(𝑥-8)
𝑥+8=3𝑥-24
𝑥-3x=-24-8
-2𝑥=-30
– 𝑥=-16 km/h
(Here minus sign is immaterial)
Q 3584) A sailor sails a distance of 48 km along the flowof a river in 8 hr. If it takes 12 hr to return the same distance. Find the speed of the flow of the river.
(A) 1km/hr (B) 2km/hr (C) 3km/hr (D) 4km/hr
Ans: (A) 1km/hr
Solution:
Formula for calculating the speed of the flow of the river or speed of stream is 1/2 (Downstream Speed-Upstream Speed)
Here, Downstream Speed is 48 km/8hr=6km/hr and Upstream Speed is 48km/12hr=4km/hr.
∴ 1/2(6-4) = 1/2×2=1km/hr
Q 3585) A boat covers a distance of 30 km downstream in 2 hr, while it takes 6 hr to cover the same distance upstream. The speed of boat is?
(A) 5km/hr (B) 7.5km/hr (C) 10km/hr (D) 12.5km/hr
Ans: (C) 10km/hr
Solution:
The formula for Speed of boat in still water is (Downstream Speed+Upstream Speed)/2
Here, Downstream Speed is 30km/2hr=15km/hr
and Upstream Speed is 30km/6hr=5km/hr
By putting figures in formula, (15+5)/2 =20/2 = 10km/hr