Ratio and Proportion — Multiple Choice Questions

The ratio of 2 m to 400 cm is:

1. 1 : 2

2. 2 : 1

3. 1 : 200

4. 200 : 1

Answer

As 1 m = 100 cm

2 m = 2 × 100 cm = 200 cm.

Ratio of 2 m to 400 cm = 200 : 400 = 1 : 2.

Hence, option 1 is the correct option.

$\dfrac{1}{2} : \dfrac{1}{3}$ is equivalent to:

1. 2 : 3

2. 3 : 2

3. 5 : 6

4. 6 : 5

Answer

$\dfrac{1}{2} : \dfrac{1}{3}$

Multiply both terms by 6

$= \dfrac{1}{2} \times 6 : \dfrac{1}{3} \times 6$

= 3 : 2.

Hence, option 2 is the correct option.

If A : B = 3 : 5 and B : C = 15 : 23, then A : C is:

1. 3 : 23

2. 23 : 3

3. 9 : 23

4. 5 : 23

Answer

A : B = 3 : 5 and B : C = 15 : 23

$\dfrac{A}{C} = \dfrac{A}{B} \times \dfrac{B}{C} = \dfrac{3}{5} \times \dfrac{15}{23} = \dfrac{45}{115} = \dfrac{9}{23}$

So, A : C = 9 : 23

Hence, option 3 is the correct option.

If A : B : C = 8 : 6 : 3 and C = 24, then B is equal to:

1. 48

2. 18

3. 12

4. none of these

Answer

Given, A : B : C = 8 : 6 : 3

Let A = 8x, B = 6x and C = 3x.

Given, C = 24

⇒ 3x = 24

⇒ x = $\dfrac{24}{3}$ = 8

∴ B = 6x = 6 × 8 = 48

Hence, option 1 is the correct option.

Mohit's salary increases in the ratio 4 : 7. If his original salary is ₹ 2,000; his new salary is:

1. ₹ 4,000

2. ₹ 6,000

3. ₹ 7,000

4. ₹ 3,500

Answer

Let the original salary be ₹ 4x and the new salary be ₹ 7x.

Original salary = ₹ 2,000

4x = 2000

x = $\dfrac{2000}{4}$ = 500

New salary = 7x = 7 × ₹ 500 = ₹ 3,500

Hence, option 4 is the correct option.

If 8 : x = $\dfrac{1}{3} : \dfrac{1}{2}$, the value of x is:

1. $\dfrac{1}{2}$

2. $\dfrac{1}{3}$

3. 12

4. 48

Answer

Given,

8 : x = $\dfrac{1}{3} : \dfrac{1}{2}$

Product of extremes = Product of means

$8 \times \dfrac{1}{2} = x \times \dfrac{1}{3}$

4 = $\dfrac{x}{3}$

x = 12.

Hence, option 3 is the correct option.

The fourth proportion to 6, 8 and 10 is:

1. $\dfrac{3}{40}$

2. $\dfrac{40}{3}$

3. 4.8

4. $\dfrac{15}{2}$

Answer

Let the fourth proportional to a, b and c be x, then a : b :: c : x, where a = 6, b = 8, c = 10.

⇒ 6 : 8 :: 10 : x

Here, the extremes are 6 and x, and the means are 8 and 10.

Product of extremes = Product of means

⇒ 6 × x = 8 × 10

$\Rightarrow x = \dfrac{8 \times 10}{6} \\[1em] = \dfrac{80}{6} \\[1em] = \dfrac{40}{3}$

Hence, option 2 is the correct option.

The third proportion to 2 : 1 is:

1. 2

2. 1

3. $\dfrac{1}{2}$

4. $\dfrac{1}{3}$

Answer

Let the third proportional to a and b be x, then a, b and x are in continued proportion, i.e. a : b :: b : x, where a = 2, b = 1.

⇒ 2 : 1 :: 1 : x

Here, the extremes are 2 and x, and the means are 1 and 1.

Product of extremes = Product of means

⇒ 2 × x = 1 × 1

$\Rightarrow x = \dfrac{1 \times 1}{2} \\[1em] = \dfrac{1}{2}$

Hence, option 3 is the correct option.

On a map, 22 m is represented by 3 cm, then what length on map represents 132 m?

1. $\dfrac{1}{2}$ cm

2. 6 cm

3. 48 cm

4. none of these

Answer

Let the length on the map representing 132 m be x cm.

The actual lengths and the lengths on the map are in proportion.

⇒ 22 : 3 :: 132 : x

Product of extremes = Product of means

⇒ 22 × x = 3 × 132

$\Rightarrow x = \dfrac{3 \times 132}{22} \\[1em] = \dfrac{396}{22} \\[1em] = 18 \text{ cm}$

Since 18 cm is not among options 1, 2 and 3, the correct choice is "none of these".

Hence, option 4 is the correct option.

$\dfrac{1}{3} : \dfrac{1}{6} : \dfrac{1}{8}$ is equivalent to:

1. 3 : 6 : 8

2. 8 : 6 : 3

3. 6 : 3 : 8

4. 8 : 4 : 3

Answer

L.C.M. of the denominators 3, 6 and 8 is 24.

Multiply each term by 24:

$\dfrac{1}{3} \times 24 : \dfrac{1}{6} \times 24 : \dfrac{1}{8} \times 24$

= 8 : 4 : 3

Hence, option 4 is the correct option.

If A = 2B = 3C then A : B : C is equal to:

1. 1 : 2 : 3

2. 3 : 2 : 1

3. 6 : 3 : 2

4. 2 : 3 : 6

Answer

Let A = 2B = 3C = k.

Then A = k, B = $\dfrac{k}{2} \text{ and } C = \dfrac{k}{3}$.

A : B : C = $k : \dfrac{k}{2} : \dfrac{k}{3} = 1 : \dfrac{1}{2} : \dfrac{1}{3}$

Multiply each term by 6:

$1 \times 6 : \dfrac{1}{2} \times 6 : \dfrac{1}{3} \times 6$

= 6 : 3 : 2.

Hence, option 3 is the correct option.

If A : B = 3 : 4 and A + B = 35, then B is equal to:

1. 21

2. 15

3. 2

4. 20

Answer

Let A = 3x and B = 4x.

A + B = 35

3x + 4x = 35

7x = 35

x = $\dfrac{35}{7}$ = 5

B = 4x = 4 × 5 = 20

Hence, option 4 is the correct option.

Which is greater, 2 : 3 or 3 : 4 ?

1. 2 : 3

2. 3 : 4

3. none of these

Answer

$2 : 3 = \dfrac{2}{3} \text{ and } 3 : 4 = \dfrac{3}{4}.\\[1em] \text { L.C.M. of 3 and 4 is 12.}\\[1em] \dfrac{2}{3} = \dfrac{2 \times 4}{3 \times 4} = \dfrac{8}{12}\\[1em] \dfrac{3}{4} = \dfrac{3 \times 3}{4 \times 3} = \dfrac{9}{12}\\[1em]$

Clearly, $\dfrac{9}{12} \gt \dfrac{8}{12}$, so (3 : 4) > (2 : 3).

Hence, option 2 is the correct option.

In a piece of paper, rectangular in shape, the ratio of its length to its breadth is 8 : 5. If the breadth is 12.5 cm; the length is:

1. 20 cm

2. 40 cm

3. 37.5 cm

4. 1.6 cm

Answer

Let the length be 8x and the breadth be 5x.

Breadth = 12.5 cm

5x = 12.5

x = $\dfrac{12.5}{5}$ = 2.5

Length = 8x = 8 × 2.5 = 20 cm

Hence, option 1 is the correct option.

The ratio of the number of faces of a cube to the number of edges in it is:

1. 1 : 2

2. 1 : 3

3. 2 : 1

4. 3 : 1

Answer

Number of faces of a cube = 6

Number of edges of a cube = 12

Ratio = 6 : 12 = 1 : 2

Hence, option 1 is the correct option.