A boat sails 15 km of a river towards upstream in 5 hours. How long will it take to cover the same distance downstream, if the speed of current is one-fourth the speed of the boat in still water:

Correct Answer: Rs. 200

Explanation:

F = B D × T D B D - T D = 200 × 100 200 - 100 = 200 × 100 100 = R s . 200

Correct Answer: Rs. 1600

Explanation:

Since the compound interest is taken here,

 

  P W 1 + 5 100 2 = 1764

 

=> PW = 1600

Correct Answer: Rs. 34

Explanation:

B G = T D 2 P W = ( 340 ) 2 3400 = R s . 34

Correct Answer: 96

Explanation:

T.D. = P.W. x B.G. = 576 x 16 = 96.

Correct Answer: 4 months

Explanation:

S.I on Rs 1800 = T.D on Rs 1872

P.W of Rs 1872 is Rs 1800

Rs 72 is S.I on Rs 1800 at 12%

Time = (100 * 72)/(12 * 1800)

= 1/3 years = 4 months

Correct Answer: 4 2⁄3 Kmph

Explanation:

Let man’s rate upstream be x km/hr. Then his rate downstream is 3 x km/hr Given: Speed in still water = 9 (1/3) = 28/3 km/hr i.e, ½ (a+b) = 28/3 km/hr ½ (x+3x) = 28/3 2x = 28/3 x = 28/ 2 x 3 = 14/3 km/hr rate upstream b = 14/3 km/hr and rate downstream a = 14/3 x 3 = 14 km/hr speed of the current = ½ (a-b) = ½ (14 – 14/3) = ½ (42-14/3) = 28/6 = 4 (2/3) km/hr

Correct Answer: 180 km

Explanation:

Speed in downstream = (14 + 4) km/hr = 18 km/hr;

Speed in upstream = (14 ? 4) km/hr = 10 km/hr.

Let the distance between A and B be x km. Then,

x/18 + (x/2)/10 = 19 ? x/18 + x/20 = 19 ? x = 180 km.

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.

Correct Answer: 16 h

Explanation:

If t1 and t2 are the upstream and down stream times. Then time taken in still water is given by 

2 × t 1 × t 2 t 1 + t 2 = 2 × 12 × 24 36 = 16 h

Correct Answer: 6 kmph

Explanation:

Speed of the stream = 1
Motor boat speed in still water be = x kmph
Down Stream = x + 1 kmph
Up Stream = x - 1 kmph
[35/(x + 1)] + [35/(x - 1)] = 12
x = 6 kmph