Ratio and Proportion — Multiple Choice Questions

The ratio of 4 litres to 900 mL is

1. 4 : 9
2. 40 : 9
3. 9 : 40
4. 20 : 9

Answer

4 litres = 4 x 1000 ml = 4000 ml

Ratio = $\dfrac{4000}{900} = \dfrac{40}{9}$ = 40 : 9.

∴ Option 2 is the correct option.

When the number 210 is increased in the ratio 5 : 7, then the new number is

1. 150
2. 180
3. 294
4. 420

Answer

Let new number be x. Since, 210 is increased in the ratio 5 : 7,

$\therefore \dfrac{210}{x} = \dfrac{5}{7} \\[0.5em] \Rightarrow x = 210 \times \dfrac{7}{5} \\[0.5em] \Rightarrow x = 294.$

∴ Option 3 is the correct option.

Two numbers are in the ratio 7 : 9. If the sum of the numbers is 288, then the smaller number is

1. 126
2. 162
3. 112
4. 144

Answer

Since, two numbers are in the ratio 7 : 9, let the numbers be 7x, 9x.

Given, the sum of two numbers = 288.

∴ 7x + 9x = 288
⇒ 16x = 288
⇒ x = $\dfrac{288}{16}$
⇒ x = 18.

Smaller number = 7x = 126.

∴ Option 1 is the correct option.

The ratio of number of edges of a cube to the number of its faces is

1. 2 : 1
2. 1 : 2
3. 3 : 8
4. 8 : 3

Answer

Number of edges in a cube = 12

Number of faces in cube = 6

Ratio of number of edges to the number of faces = $\dfrac{12}{6} = \dfrac{2}{1}$ = 2 : 1.

∴ Option 1 is the correct option.

If x, 12, 8 and 32 are in proportion, then the value of x is

1. 6
2. 4
3. 3
4. 2

Answer

Given, x : 12 : : 8 : 32

$\Rightarrow \dfrac{x}{12} = \dfrac{8}{32} \\[0.5em] \Rightarrow x = 12 \times \dfrac{8}{32} \\[0.5em] \Rightarrow x = 3.$

∴ Option 3 is the correct option.

The fourth proportional to 3, 4, 5 is

1. 6

2. $\dfrac{20}{3}$

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

4. $\dfrac{12}{5}$

Answer

Let the fourth proportional be x.

So, the numbers 3, 4, 5, x are in proportion.

$\therefore 3 : 4 : : 5 : x \\[0.5em] \Rightarrow \dfrac{3}{4} = \dfrac{5}{x} \\[0.5em] \Rightarrow x = 5 \times \dfrac{4}{3} \\[0.5em] \Rightarrow x = \dfrac{20}{3}.$

∴ Option 2 is the correct option.

The third proportional to $6\dfrac{1}{4}$ and 5 is

1. 4

2. $7\dfrac{1}{2}$

3. 3

4. none of these

Answer

Let the third proportional be x.

Hence, the numbers $6\dfrac{1}{4}$, 5, x are in continued in proportion.

$\therefore \dfrac{25}{4} : 5 : : 5 : x \\[0.5em] \Rightarrow \dfrac{\dfrac{25}{4}}{5} = \dfrac{5}{x} \\[0.5em] \Rightarrow \dfrac{25}{20} = \dfrac{5}{x} \\[0.5em] \Rightarrow x = 5 \times \dfrac{20}{25} \\[0.5em] \Rightarrow x = 4.$

∴ Option 1 is the correct option.

The mean proportional between $\dfrac{1}{2}$ and 128 is

1. 64
2. 32
3. 16
4. 8

Answer

Let the mean proportional be x.

Hence, the numbers are $\dfrac{1}{2}$, x and 128 are in continued in proportion.

$\therefore \dfrac{1}{2} : x : : x : 128 \\[0.5em] \Rightarrow \dfrac{\dfrac{1}{2}}{x} = \dfrac{x}{128} \\[0.5em] \Rightarrow x^2 = \dfrac{1}{2} \times 128 \\[0.5em] \Rightarrow x^2 = 64 \\[0.5em] \Rightarrow x = \sqrt{64} \\[0.5em] \Rightarrow x = 8.$

∴ Option 4 is the correct option.

The table shows the values of x and y, where x is proportional to y. What are the values of M and N ?

1. M = 4, N = 9

2. M = 9, N = 3

3. M = 9, N = 4

4. M = 12, N = 0

Answer

Given, x is proportional to y.

$\Rightarrow \dfrac{6}{M} = \dfrac{12}{18} \\[1em] \Rightarrow M = \dfrac{6 \times 18}{12} \\[1em] \Rightarrow M = \dfrac{108}{12} \\[1em] \Rightarrow M = 9. \\[1.5em] \dfrac{12}{18} = \dfrac{N}{6} \\[1em] \Rightarrow N = \dfrac{12 \times 6}{18} \\[1em] \Rightarrow N = \dfrac{72}{18} \\[1em] \Rightarrow N = 4.$

Hence, Option 3 is the correct option.

The given table shows the distance covered and the time taken by a train moving at a uniform speed along a straight track.

The values of x and y are :

1. x = 4, y = 150

2. x = 3, y = 100

3. x = 4, y = 100

4. x = 3, y = 150

Answer

Speed = $\dfrac{\text{Distance}}{\text{Time}}$

Average speed = $\dfrac{60}{2}$ = 30 km/hr

$\Rightarrow \dfrac{90}{x} = 30 \\[1em] \Rightarrow x = \dfrac{90}{30} = 3. \\[1em] \phantom{\Rightarrow} \dfrac{y}{5} = 30 \\[1em] \Rightarrow y = 30 \times 5 = 150.$

Hence, Option 4 is the correct option.

A mixture of paint is prepared by mixing 2 parts of red pigments with 5 parts of the base. Using the given information in the following table, find the values of a, b and c to get the required mixture of paint.

1. a = 10, b = 10, c = 10

2. a = 5, b = 2, c = 5

3. a = 10, b = 5, c = 10

4. a = 10, b = 5, c = 15

Answer

Given,

2 parts of red pigments is mixed with 5 parts of the base.

$\therefore \dfrac{4}{a} = \dfrac{2}{5} \\[1em] \Rightarrow a = \dfrac{4 \times 5}{2} = \dfrac{20}{2} = 10. \\[1em] \therefore \dfrac{b}{12.5} = \dfrac{2}{5} \\[1em] \Rightarrow b = \dfrac{2}{5} \times 12.5 = 2 \times 2.5 = 5 \\[1em] \therefore \dfrac{6}{c} = \dfrac{2}{5} \\[1em] \Rightarrow c = \dfrac{6 \times 5}{2} = 3 \times 5 = 15.$

Hence, Option 4 is the correct option.