Boats & Streams Model Questions Set 1 Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (c)

Let the distance = d km

Time taken to row upstream '$t_1$ ' = $d/{5-3}=d/2$ …(1)

Time taken to row downstream $'t_2 '$ = $d/{5+3}=d/8$ …(2)

$t_1 + t_2$ = 5 (Given)

∴ $d/2+ d/8 = 5$

⇒ ${4d+d}/8=5⇒ d=8km $

∴ Distance of the place = 8 km.

Answer: (b)

If six coins are tossed, then the total no. of outcomes = $(2)^6$ = 64

Now, probability of getting no tail = $1/{64}$

Probability of getting at least one tail = 1 - $1/{64} = {63}/{64}$

Answer: (b)

There can be 3 cases :

I. When one dice shows 2.

II. When two dice shows 2.

III. When three dices shows 2.

Case I : The dice which shows 2 can be selected out of the 3 dices in $^3C_1$ ways.

Remaining 2 dices can have any 5 numbers except 2. So number of ways for them = $^5C_1$ each, so no of ways when one dice shows 2 = $^3C_1 × ^5C_1 × ^5C_1$ .

Case II : Two dices, showing 2 can be selected out of the 3 dices in $^3C_2$ ways and the rest one can have any 5 numbers except 2, so number of ways for the remaining 1 dice = 5.

So, number of ways, when two dices show

2 = $^3C_2$ × 5

Case III : When three dices show 2 then these can be selected in $^3C_3$ ways.

So, number of ways, when three dices show

2 = $^3C_3$ = 1

As, either of these three cases are possible.

Hence, total number of ways

= (3 × 5 × 5) + (3 × 5) + 1 = 91

Answer: (c)

Speed of the boat downstream =$120/5$ = 24 km/h

Ratio of speeds of boat and stream = 2 : 1

∴ Speed of the stream = $1/3×24$ = 8 km/h

Answer: (c)

Let upstream rate = x km/hr,

downstream rate = y km/hr

∴ $24/x+36/y=6$ ...(1)

$36/x+24/y=13/2$ ...(2)

Add (1) and (2) , we get

$60{(1/x+1/y)}=25/2 ⇒ 1/x+1/y=5/24$ ...(3)

Subtract (1) from (2)

$12{(1/x-1/y)}=1/2 ⇒ 1/x-1/y=1/24$ ...(4)

Add (3) and (4)

$2/x=6/24⇒x=8$

rom (3) y = 12

∴ Velocity of current = $1/2{(y-x)}=1/2{(12-8)}$=2km/hr

Answer: (b)

Let speed in still water = x km/h

Speed of stream = 2km/h

∴ $10/{x+2}+10/{x-2}=55/60$

$10x+10x=11/12(x^2-4)$

$11x^2-240x-44=0$

x = 22

∴ speed in still water = 22 km/h