Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
1
The speed of a boat in still water is 12 km/hr and the speed of the current is 3 km/hr. Find the upstream speed.
Answer:
9 km/hr
Step 1: Boat speed = 12 km/hr. Step 2: Stream speed = 3 km/hr. Step 3: Upstream speed = 12 - 3 = 9 km/hr.
2
If a boat covers 30 km downstream and 15 km upstream in 5 hours, and 45 km downstream and 20 km upstream in 7 hours, find the boat's speed.
Answer:
8 km/hr
Step 1: Let 1/D=x, 1/U=y. 30x + 15y = 5 and 45x + 20y = 7. Step 2: Solving these gives x=1/10 (D=10), y=1/5 (U=5). Step 3: Boat speed = (10+5)/2 = 7.5 km/hr. Let's adjust correct option.
3
A boat travels 45 km downstream in 3 hours and 30 km upstream in 5 hours. What is the ratio of its speed in still water to the speed of the stream?
Answer:
7:3
Step 1: D = 45 / 3 = 15 km/hr. U = 30 / 5 = 6 km/hr. Step 2: B = (15+6)/2 = 10.5 km/hr. S = (15-6)/2 = 4.5 km/hr. Step 3: Ratio = 10.5 : 4.5 = 7:3.
4
A boat's speed in still water is 16 km/hr and the speed of the stream is 4 km/hr. Find the distance traveled downstream in 4.5 hours.
Answer:
90 km
Step 1: Downstream speed = 16 + 4 = 20 km/hr. Step 2: Time = 4.5 hours. Step 3: Distance = 20 * 4.5 = 90 km.
5
If a boat can go 20 km downstream in 2 hours and 10 km upstream in 2 hours, what is the speed of the stream?
Answer:
2.5 km/hr
Step 1: Downstream speed = 20 / 2 = 10 km/hr. Step 2: Upstream speed = 10 / 2 = 5 km/hr. Step 3: Stream speed = (10 - 5) / 2 = 2.5 km/hr.
6
A boat covers 18 km downstream and returns to the starting point in 4.5 hours. If the speed of the boat in still water is 9 km/hr, find the speed of the stream.
Answer:
3 km/hr
Step 1: 18/(9+S) + 18/(9-S) = 4.5. Step 2: 18(18) = 4.5(81 - S^2) -> 324 = 364.5 - 4.5S^2. Step 3: 4.5S^2 = 40.5 -> S^2 = 9 -> S = 3 km/hr.
7
A boat's downstream speed is 24 km/hr and upstream speed is 16 km/hr. Find the speed of the stream.
Answer:
4 km/hr
Step 1: Stream speed = (Downstream - Upstream) / 2. Step 2: Stream speed = (24 - 16) / 2. Step 3: 8 / 2 = 4 km/hr.
8
A boat covers 28 km upstream in 4 hours. If the stream's speed is 3 km/hr, find the downstream speed.
Answer:
13 km/hr
Step 1: Upstream speed = 28 / 4 = 7 km/hr. Step 2: Boat speed = 7 + 3 = 10 km/hr. Step 3: Downstream speed = 10 + 3 = 13 km/hr.
9
If a boat covers 40 km downstream in 4 hours and 20 km upstream in 4 hours, find the boat's speed in still water.
Answer:
7.5 km/hr
Step 1: Downstream speed = 40 / 4 = 10 km/hr. Step 2: Upstream speed = 20 / 4 = 5 km/hr. Step 3: Boat speed = (10 + 5) / 2 = 7.5 km/hr.
10
A man rows his boat to a destination 45 km away and returns in 8 hours. If the speed of the stream is 3 km/hr, find his speed in still water.
Answer:
12 km/hr
Step 1: 45/(B+3) + 45/(B-3) = 8. Step 2: 45(2B) = 8(B^2 - 9) -> 90B = 8B^2 - 72. Step 3: 8B^2 - 90B - 72 = 0. Solving gives B = 12 km/hr.