**Question 1 :**

A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the length of broken part.

(A) 13 m (B) 15 m (C) 18 m

**Solution :**

Here,

AC^{2} = AB^{2} + BC^{2}

AC^{2} = 12^{2} + 5^{2}

AC^{2} = 144 + 25 ==> 169

AC = √169 = √13 ⋅ 13

AC = 13 m

So, the length of the broken part is 13 m.

**Question 2 :**

Find the ratio of 3 km to 300 m.

(A) 10:1 (B) 1:10 (C) 2:5

**Solution :**

We can compare two ratios of the same kind only.So,let us convert km to meters.

1000 m = 1 km

3 km = 3 x 1000 = 3000 m

= 3000 : 300

= 10 : 1

So, the required ratio is 10 : 1.

**Question 3 :**

Find BC, if the area of the triangle ABC is 36 cm^{2} and the height AD is 3 cm.

(A) 18 cm (B) 24 cm (C) 10 cm

**Solution :**

BC = Base of the triangle

AD = Height of the triangle = 3 cm

Area of triangle = (1/2) x Base x Height

= (1/2) x BC x AD

36 = (1/2) x BC x 3

(36 ⋅ 2)/3 = BC

BC = 24 cm

So, the base of the triangle is 24 cm.

**Question 4 :**

How many times a wheel of radius 28 cm must rotate to go 352 m? (Take π = 22/7)

(A) 300 times (B) 200 times (C) 400 times

**Solution :**

Radius of wheel = 28 cm

Distance to be covered = 352 m = 35200 cm

Distance covered in one revolution = 2πr

= 2 ⋅ (22/7) ⋅ 28

= 176 cm

Number of revolutions

= Distance to be covered/Distance covered in one revolution

= 35200/176

= 200 times

So, the wheel has to be rotated 200 times to go 352 m.

**Question 5 :**

A rectangular park is 45 m long and 30 m wide. The path 2.5 m wide is constructed outside the park. Find the area of that path.

(A) 400 m^{2} (B) 200 m^{2} (C) 150 m^{2}

**Solution :**

Area of path

= Area of rectangle ABCD - Area of rectangle abcd

In abcd : Length = 45 m Width = 30 m |
In ABCD : Length AB = 45 + 2.5 + 2.5 = 50 m Width BC = 30 + 2.5 + 2.5 = 35 m |

Area of path = 50 ⋅ 35 - 45 ⋅ 30

= 1750 - 1350

= 400 m^{2}

So, the area of the path is 400 m^{2} .

**Question 6 :**

Find the value of the expression a^{2} + 2 ab + b^{2}

if a = 3, b = 2

**(A) 27 (B) 35 (C) 25**

**Solution :**

a^{2} + 2 ab + b^{2} = 3^{2} + 2 (3)(2) + 2^{2}

= 9 + 12 + 4

= 25

So, the value of the given expression is 25.

**Question 7 :**

In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?

**(A) 27 (B) 35 (C) 25**

**Solution :**

There are 3 computers for every 6 students

Number of computers for 1 student = 3/6 = 1/2

Number of computers for 24 students = (1/2) 24

= 12 computers

So, every 24 students need 12 computers.

**Question 8 :**

The side of an equilateral triangle is 3.5 cm. Find its perimeter.

(A) 5.9 cm (B) 2.7 cm (C) 10.5 cm

**Solution**

Side length of equilateral triangle = 3.5 cm

Perimeter of equilateral triangle = 3a

= 3 (3.5)

= 10.5 cm

So, the perimeter of the equilateral triangle is 10.5 cm.

**Question 9 :**

Find the value of 2.5 + 5.1

(A) 7.6 (B) 2.5 (C) 8.2

**Solution**

oooooooooooooooooooooo2.5 (+) ooooooooooooooooooooooo

oooooooooooooooooooooo5.1ooooooooooooooooooooooooooo

oooooooooooooooooooo_____ooooooooooooooooooooooooo

oooooooooooooooooooo07.60000oooooooooooooooooooooo

oooooooooooooooooooo_____ooooooooooooooooooooooooo

**Question 10 :**

The wood cutter took 12 minutes to make 3 pieces of a block of wood. How long would be needed to make 5 such pieces?

(A) 50 minutes (B) 20 minutes (C) 30 minutes

**Solution :**

Time taken for wood cutter to cut block of wood into 3 pieces = 12 minutes

Time taken for wood cutter to cut a block of wood into 1 piece

= 12/3 = 4 minutes

Time taken for wood cutter to cut a block of wood as 5 pieces

= 4 (5) = 20 minutes

So the time taken is 20 minutes.

If you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**