Discussion
Home ‣ Aptitude ‣ Boats and Streams See What Others Are Saying!
- Question
A man went downstream for 28 km in a motor boat and immediately returned. It took the man twice as long to make the return trip. If the speed of the river flow were twice as high, the trip downstream and back would take 672 minutes. Find the speed of the boat in still water and the speed of the river flow.
Options- A. 12 km/hr, 3 km/hr
- B. 9 km/hr, 3 km/hr
- C. 8 km/hr, 2 km/hr
- D. 9 km/hr, 6 km/hr
- Correct Answer
- 9 km/hr, 3 km/hr
Explanation
Let's call the speed of the boat in still water "b" and the speed of the river flow "r".
When the man goes downstream, he travels with the current, so his effective speed is b + r. When he goes upstream, he travels against the current, so his effective speed is b - r.
We know that the man traveled 28 km downstream and then immediately returned, so his total distance traveled is 56 km. We also know that it took him twice as long to make the return trip, so his time going upstream was twice his time going downstream.
Using the formula distance = rate x time, we can set up two equations:
28 = (b + r) * t1
28 = (b - r) * 2t1
where t1 is the time it took the man to go downstream.
Simplifying the second equation, we get:
14 = (b - r) * t1
Now let's consider what happens if the speed of the river flow is doubled. The new effective speed downstream would be b + 2r, and the new effective speed upstream would be b - 2r. The total distance traveled is still 56 km. We can set up two more equations:
56 = (b + 2r) * t2
56 = (b - 2r) * 2t2
where t2 is the new total time it takes to make the trip downstream and back.
Simplifying the second equation, we get:
28 = (b - 2r) * t2
Now we have four equations and four unknowns (b, r, t1, and t2). We can solve for them using substitution and elimination.
From the first equation, we can solve for t1:
t1 = 28 / (b + r)
From the second equation, we can solve for t1 in terms of t2:
t1 = 14 / (b - r)
Setting these two expressions for t1 equal to each other and simplifying, we get:
(b + r) / (b - r) = 2
Solving for r in terms of b, we get:
r = b / 3
Now we can substitute this expression for r into any of the four equations to solve for the other variables. Let's use the first equation:
28 = (b + r) * t1
28 = (4b/3) * t1
t1 = 21 / (2b)
Now we can use this expression for t1 to solve for t2 in terms of b:
t2 = 42 / (2b - 4r)
t2 = 42 / (2b - 4b/3)
t2 = 126 / b
Finally, we can use the third equation to solve for b:
56 = (b + 2r) * t2
56 = (4b/3 + 2b/3) * 126 / b
56 = 2 * 126
b = 9
So the speed of the boat in still water is 9 km/h, and the speed of the river flow is b/3 = 3 km/h. - 1. Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
Options- A. 2 : 3
- B. 1 : 1
- C. 3 : 4
- D. 4 : 3 Discuss
- 2. A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
Options- A. 65 sec
- B. 89 sec
- C. 100 sec
- D. 150 sec Discuss
- 3. What was the day of the week on 17th June, 1998?
Options- A. Monday
- B. Tuesday
- C. Wednesday
- D. Thursday Discuss
- 4. The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:
Options- A. 279
- B. 283
- C. 308
- D. 318 Discuss
- 5. 1872/ ? ? = 234
Options- A. 324
- B. 64
- C. 8
- D. 256 Discuss
- 6. For every 4 leaps taken by a dog, a cat takes 5 leaps in the same time. But distance covered in 3 leaps of dog is same as that of 4 leaps of cat. Then what is the ratio of speed of dog and cat?
Options- A. 15 : 14
- B. 16 :15
- C. 12 :11
- D. 10 : 9 Discuss
- 7. A come of height 7 cm and base radius 3 cm is curved from a rectangular block of wood 10 cm x 5 cm x 2 cm. The percentage of wood wasted is?
Options- A. 34%
- B. 46%
- C. 54%
- D. 66% Discuss
- 8. 1, 9, 25, 49, 81,?
Options- A. 90
- B. 135
- C. 121
- D. 125 Discuss
- 9. An accurate clock shows the time as 3:00 after hour hand has moved 135°, the time would be?
Options- A. 7:30
- B. 6:30
- C. 8:00
- D. 9:30 Discuss
- 10. P.V. Narsihma Rao was elected party leader on 29th may, 1991. What was the day of the week?
Options- A. Tuesday
- B. Friday
- C. Wednesday
- D. Sunday Discuss
More questions
Correct Answer: 4 : 3
Explanation:
| 5% of A + 4% of B = | 2 | (6% of A + 8% of B) |
| 3 |
| ⟹ | 5 | A + | 4 | B | = | 2 | ❨ | 6 | A + | 8 | B | ❩ |
| 100 | 100 | 3 | 100 | 100 |
| ⟹ | 1 | A + | 1 | B | = | 1 | A + | 4 | B |
| 20 | 25 | 25 | 75 |
| ⟹ | ❨ | 1 | - | 1 | ❩ A = | ❨ | 4 | - | 1 | ❩ B |
| 20 | 25 | 75 | 25 |
| ⟹ | 1 | A = | 1 | B |
| 100 | 75 |
| A | = | 100 | = | 4 | . |
| B | 75 | 3 |
∴ Required ratio = 4 : 3
Correct Answer: 89 sec
Explanation:
| Speed = | ❨ | 240 | ❩m/sec = 10 m/sec. |
| 24 |
| ∴ Required time = | ❨ | 240 + 650 | ❩sec = 89 sec. |
| 10 |
Correct Answer: Wednesday
Explanation:
17 th June, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)
Odd days in 1600 years = 0
Odd days in 300 years = (5 x 3) ≡ 1
97 years has 24 leap years + 73 ordinary years.
Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.
Jan. Feb. March April May June (31 + 28 + 31 + 30 + 31 + 17) = 168 days
∴ 168 days = 24 weeks = 0 odd day.
Total number of odd days = (0 + 1 + 2 + 0) = 3.
Given day is Wednesday.
Correct Answer: 308
Explanation:
| Other number = | ❨ | 11 x 7700 | ❩ | = 308. |
| 275 |
Correct Answer: 64
Explanation:
Let 1872/?N = 234.
Then ?N = 1872/234 = 8
? N = 8 x 8 = 64
Correct Answer: 16 :15
Explanation:
Let distance covered by dog in 1 leap is x and
Distance covered by cat in 1 leap is y
Then, 3x = 4y
? x= 4/3y
Now, Ratio of speed of dog and cat = Ratio of distance covered by them in the same time = 4x : 5y
= 16/3y : 5y
= 16 : 15
Correct Answer: 34%
Explanation:
Total volume of cuboid = (10 x 5 x 2) cm3
= 100 cm3
Volume curved = 1/3 x (22/7) x 3 x 3 x 7 cm3
= 66 cm3
% of wood wasted = (100 - 66)% = 34 %
Correct Answer: 90
Explanation:
Series pattern
12, 32, 52, 72, 92, 112
So missing term = 112 = 121
Correct Answer: 7:30
Explanation:
Angle of 360° is covered by hour hand in 12 h .
So, angle of 135° is covered by hour hand in 12/360° x 135° = 4.5 h
Thus, required time = (3 + 4.5)h = 7.5 h = 7 : 30
Correct Answer: Wednesday
Explanation:
Try yourself. It was Wednesday.
Comments
There are no comments.More in Aptitude:
Programming
Copyright ©CuriousTab. All rights reserved.