Correct Answers: | |

Wrong Answers: | |

Unattempted: |

### Question 1

The speed of a boat in still water, the upstream speed of the boat and the downstream speed of the boat form an A.P.(Arithmetic Progression) whose middle term is $1{1/5}$. What is the speed of the boat in still water?

**A**

$1{1/5}$ units.

**B**

$2{3/4}$ units.

**C**

$2{2/7}$ units.

**D**

3 units.

**Soln.**

**Ans: a**

Let the speed of the boat in still water be u and the speed of the stream be v. The three speeds are u - v, u and u + v. They are in an A.P. with a common difference equal to v, and u as its middle term. Since u is also the speed of the boat in still water, the required answer is: $1{1/5}$.

### Question 2

A boat can travel 288 km downstream in 24 hours. If it covers the same distance upstream in 72 hours, what is the speed of the boat in still water?

**A**

8 kmph.

**B**

9 kmph.

**C**

7 kmph.

**D**

11 kmph.

**Soln.**

**Ans: a**

The downstream speed = $288/24$ = 12 km/h, and the upstream speed = $288/72$ = 4 km/h. By the shortcut method, the speed of the boat in still water is average of the downstream and upstream speeds of the boat. So the required speed = ${12 + 4}/2$ = 8 km/h.

### Question 3

The speed of an aircraft in still air is 12 km/h and rate of wind is 8 km/h. If it travels along the direction of the wind for 8 hours, what is the distance travelled by the aircraft during the journey?

### Question 4

The difference of the squares of the downstream and upstream speeds of a boat in a stream is 28. What is the product of the speed of the stream and that of the boat in still water?

**A**

7.

**B**

8.

**C**

6.

**D**

10.

**Soln.**

**Ans: a**

Let the speed of the boat in still water be u, and let v be the speed of the stream. The difference of squares of the speeds is $(u + v)^2 - (u - v)^2$, which is $u^2 + v^2 + 2uv - (u^2 + v^2 - 2uv)$ = 4uv = 28. We get uv = $28/4$ = 7.

### Question 5

The upstream journey of a boat takes 8 times the time it takes it to complete the downstream journey. What is the ratio of the speed of the boat in still water to the speed of the stream?

**A**

$1{2/7}$.

**B**

$2{2/3}$.

**C**

${2/9}$.

**D**

$3{1/3}$.

**Soln.**

**Ans: a**

Let the distance be L and the speed of the boat in still water be u, with v being the speed of the stream. We are given $L/{u - v} = 8 × L/{u + v}$. We can solve this equation for u/v to get u/v = ${8 + 1}/{8 - 1}$ = $1{2/7}$.

This Blog Post/Article "Boats and Streams Quiz Set 001" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2020-02-07. Published on: 2016-05-06