Ratio & Proportion — Multiple Choice Questions

Ratio of 350 m to 1 km is :

1. 1 : 4

2. 7 : 20

3. 7 : 15

4. 17 : 20

Answer

Both quantities must be in the same unit.

1 km = 1000 m

Ratio = 350 : 1000

H.C.F. of 350 and 1000 is 50.

$\dfrac{350 \div 50}{1000 \div 50} = \dfrac{7}{20} = 7 : 20$

Hence, option 2 is the correct option.

Simple ratio of $\dfrac{7}{3} : 3 : \dfrac{5}{4}$ is :

1. 7 : 3 : 5

2. 3 : 1 : 4

3. 28 : 36 : 15

4. 36 : 28 : 15

Answer

Given ratio = $\dfrac{7}{3} : 3 : \dfrac{5}{4}$

L.C.M. of the denominators 3, 1 and 4 is 12.

Multiplying each term by 12 :

$\dfrac{7}{3} \times 12 : 3 \times 12 : \dfrac{5}{4} \times 12 = 28 : 36 : 15$

Hence, option 3 is the correct option.

Natural numbers p, q, r and s are in proportion, if :

1. p × q = r × s

2. p × r = q × s

3. p × s = q × r

4. none of these

Answer

If p, q, r and s are in proportion, i.e. p : q : : r : s, then

product of extremes = product of means

⇒ p × s = q × r

Hence, option 3 is the correct option.

In a proportion, the two extreme terms are 18 and 15. If one of the two means is 30, the other mean term is :

1. 9

2. 18

3. 5

4. 27

Answer

In a proportion, product of extremes = product of means.

Product of extremes = 18 × 15 = 270

Let the other mean term be x.

⇒ 30 × x = 270

⇒ x = $\dfrac{270}{30}$ = 9.

Hence, option 1 is the correct option.

The angles of a triangle are in the ratio 3 : 7 : 8. The sum of its smallest and the largest angle is :

1. 150°

2. 80°

3. 110°

4. 132°

Answer

The sum of the angles of a triangle = 180°

Let the angles be 3x, 7x and 8x.

⇒ 3x + 7x + 8x = 180°

⇒ 18x = 180°

⇒ x = $\dfrac{180\degree}{18}$

⇒ x = 10°

The angles are 3 × 10° = 30°, 7 × 10° = 70° and 8 × 10° = 80°.

Smallest angle = 30° and largest angle = 80°.

Sum of the smallest and the largest angle = 30° + 80° = 110°.

Hence, option 3 is the correct option.

If 5 : 7 : : 9 : x, the value of x is :

1. 12.6

2. 14.4

3. 10.8

4. none of these

Answer

In a proportion, product of extremes = product of means.

⇒ 5 × x = 7 × 9

⇒ 5x = 63

⇒ x = $\dfrac{63}{5}$ = 12.6

Hence, option 1 is the correct option.

Two numbers are in the ratio 7 : 5 and the sum of these numbers is 126. The larger number is :

1. 126 × 7

2. 126 ÷ 1

3. 126 ÷ 12

4. $\dfrac{126}{12} × 7$

Answer

Ratio of the two numbers = 7 : 5

Let the two numbers be 7x and 5x.

⇒ 7x + 5x = 126

⇒ 12x = 126

⇒ x = $\dfrac{126}{12}$

The larger number = 7x = 7 × $\dfrac{126}{12} = \dfrac{126}{12} × 7$.

Hence, option 4 is the correct option.

The ratio of zinc and copper in an alloy is 3 : 7. If the weight of copper in the alloy is 70 g, the weight of zinc in it is :

1. 30 g

2. 100 g

3. 60 g

4. 45 g

Answer

Ratio (Zinc : Copper) = 3 : 7

Since 7 parts represent the copper, 7 parts = 70 g.

1 part = $\dfrac{70}{7}$ = 10 g.

Weight of zinc = 3 parts = 3 × 10 = 30 g.

Hence, option 1 is the correct option.

Cost of 20 identical articles is ₹ 600. Then the cost of 30 such articles is :

1. ₹ 450

2. ₹ 900

3. ₹ 750

4. none of these

Answer

Cost of 20 articles = ₹ 600

Cost of 1 article = $\dfrac{600}{20}$ = ₹ 30.

Cost of 30 articles = 30 × ₹ 30 = ₹ 900.

Hence, option 2 is the correct option.

Ratios 40 cm to 2 m and ₹ 30 to ₹ 150 form a proportion.

1. yes

2. no

3. none of these

Answer

First ratio : 40 cm to 2 m

2 m = 200 cm

40 : 200 = $\dfrac{40}{200} = \dfrac{1}{5}$ = 1 : 5

Second ratio : ₹ 30 to ₹ 150

30 : 150 = $\dfrac{30}{150} = \dfrac{1}{5}$ = 1 : 5

Since both ratios are equal to 1 : 5, they form a proportion.

Hence, option 1 is the correct option.