Ratio and Proportion MCQ Quiz - Objective Question with Answer for Ratio and Proportion - Download Free PDF

Given Ratios:

a : b = 3 : 5

b : c = c : d

a : d = 3 : 8

d = 16

Express Ratios as Fractions:

a/b = 3/5

b/c = c/d

a/d = 3/8

Use a/d to Find a:

a/16 = 3/8

a = (3/8) × 16

a = 6

Use a/b to Find b:

6/b = 3/5

3b = 6 × 5

3b = 30

b = 10

Therefore, the value of b is 10.

The Correct answer is Option 3. 

Key Points​Let the initial cash prizes received by A, B, and C be 3x, 4x, and 5x respectively, based on the initial ratio of 3:4:5.

​After the school principal gives ₹4,000 to each student, the new prizes become:

• A's prize: 3x + 4000
• B's prize: 4x + 4000
• C's prize: 5x + 4000

Now, according to the new ratio of 5:6:7, the new prizes follow this ratio. Therefore, we can set up the following proportion:

= (3x + 4000) / 5 = (4x + 4000) / 6 = (5x + 4000) / 7

Let's solve for x by equating the first two terms:

= (3x + 4000) / 5 = (4x + 4000) / 6

Cross-multiply:

= 6(3x + 4000) = 5(4x + 4000)

Expanding both sides:

= 18x + 24000 = 20x + 20000

Simplifying:

= 24000 - 20000 = 20x - 18x

= 4000 = 2x

x = 2000

Now that we know x = 2000, B's initial prize is:  4x = 4 × 2000 = ₹8000

Hence, Option 3 (₹8,000) is correct.

Given:

The ratio of Mona's and Priya's present age is 9 ∶ 10.

After 4 years, the ratio of their ages becomes 11 ∶ 12.

Calculation:

Let Mona's present age be 9x and Priya's present age be 10x.

After 4 years, their ages will be 9x + 4 and 10x + 4 respectively.

According to the given condition:

\(\dfrac{9x + 4}{10x + 4} = \dfrac{11}{12}\)

⇒ 12(9x + 4) = 11(10x + 4)

⇒ 108x + 48 = 110x + 44

⇒ 2x = 4

⇒ x = 2

Mona's present age = 9x = 9 × 2 = 18 years

∴ The correct answer is option 1.

Given:

The ratio of Rs. 1, 50-paise, and 25-paise coins = 4 ∶ 5 ∶ 6.

Total amount in the bag = Rs. 32.

Formula Used:

Total amount = (Number of coins × Value of Coin) 

Calculation:

Let the number of Rs. 1 coins = 4x,

Number of 50-paise coins = 5x

Number of 25-paise coins = 6x.

Value of Rs. 1 coins = 4x × 1 = 4x

Value of 50-paise coins = 5x × 0.50 = 2.5x

Value of 25-paise coins = 6x × 0.25 = 1.5x

Total value of the coins = 4x + 2.5x + 1.5x = 8x

We are given that the total amount is Rs. 32:

8x = 32

⇒ x = 32 / 8 = 4

Number of Rs. 1 coins = 4x = 4 × 4 = 16

The number of Rs. 1 coins is 16.

Given:

x : y = 3 : 2

Calculation:

Let x = 3k and y = 2k

Substitute x and y into the expression:

\(\rm \frac{2x+3y}{5x + 7y}\)

⇒ \(\frac{2(3k) + 3(2k)}{5(3k) + 7(2k)}\)

⇒ \(\frac{6k + 6k}{15k + 14k}\)

⇒ \(\frac{12k}{29k}\)

⇒ \(\frac{12}{29}\)

The correct answer is option 3.

Given:

u : v = 4 : 7 and v : w = 9 : 7

Concept Used: In this type of question, number can be calculated by using the below formulae

Calculation:

u : v = 4 : 7 and v : w = 9 : 7

To make ratio v equal in both cases

We have to multiply the 1st ratio by 9 and 2nd ratio by 7

u : v = 9 × 4 : 9 × 7 = 36 : 63 ----(i)

v : w = 9 × 7 : 7 × 7 = 63 : 49 ----(ii)

Form (i) and (ii), we can see that the ratio v is equal in both cases

So, Equating the ratios we get,

u ∶ v ∶ w = 36 ∶ 63 ∶ 49

⇒ u ∶ w = 36 ∶ 49

When u = 72,

⇒ w = 49 × 72/36 = 98

∴ Value of w is 98

Given:

₹ 785 in the denomination of ₹ 2, ₹ 5 and ₹ 10 coins

The coins are in the ratio of 6 : 9 : 10

Calculation:

Let the number of coins of ₹ 2, ₹ 5 and ₹ 10 be 6x, 9x, and 10x respectively

⇒ (2 × 6x) + (5 × 9x) + (10 × 10x) = 785

⇒ 157x = 785

∴ x = 5

Number of coins of ₹ 5 = 9x = 9 × 5 = 45

∴ 45 coins of ₹ 5 are in the bag

Given:

A : B = 7 : 8

B : C = 7 : 9

Concept:

If N is divided into a : b, then

First part = N × a/(a + b)

Second part = N × b/(a + b)

Calculation:

A/B = 7/8      ----(i)

Also B/C = 7/9      ----(ii)

Multiply equation (i) and (ii) we get,

⇒ (A/B) × (B/C) = (7/8) × (7/9)

⇒ A/C = 49/72

∵ A : B = 49 : 56

∴ A : B : C = 49 : 56 : 72

 Alternate Method

A : B = 7 : 8 = 49 : 56

B : C = 7 : 9 = 56 : 72

⇒ A : B : C = 49 : 56 : 72

Given:

Total coin = 220

Total money = Rs. 160

There are thrice as many 1 Rupee coins as there are 25 paise coins.

Concept used:

Ratio method is used.

Calculation:

Let the 25 paise coins be 'x'

So, one rupees coins = 3x

50 paise coins = 220 – x – (3x) = 220 – (4x)

According to the questions,

3x + [(220 – 4x)/2] + x/4 =160

⇒ (12x + 440 – 8x + x)/4 = 160

⇒  5x + 440 = 640

⇒ 5x = 200

⇒ x = 40

So, 50 paise coins = 220 – (4x) = 220 – (4 × 40) = 60

∴ The number of 50 paise coin is 60.

Given:

A = 75% of B

Calculation:

A = 3/4 of B

⇒ A/B = 3/4

Let the value of A be 3x and B be 4x

So (2B – A)/A = (2 × 4x – 3x)/3x

⇒ (2B – A)/A = 5x/3x

∴ (2B – A)/A = 5/3

Short Trick:

Ratio of A : B = 3 : 4

∴ (2B – A)/A = (8 – 3) /3 = 5/3

Given:

x : y = 5 : 4

Explanation:

(x/y) = (5/4)

(y/x) = (4/5)

Now, \(\left( {\frac{x}{y}} \right):\left( {\frac{y}{x}} \right)\) = (5/4)/(4/5) = 25/16

∴ \(\left( {\frac{x}{y}} \right):\left( {\frac{y}{x}} \right)\) = 25 : 16

Given :

Ratio of two numbers is 4 : 7 

Calculations :

Let the number added to denominator and numerator be 'x' 

Now according to the question 

(4 + x)/(7 + x) = 2 : 3 

⇒ 12 + 3x = 14 + 2x 

⇒ x = 2 

∴ 2 will be added to make the term in the ratio of 2 : 3.

Given:

Ratio of two numbers is 14 : 25

Difference between them is 264

Calculation:

Let the numbers be 14x and 25x

⇒ 25x – 14x = 264

⇒ 11x = 264

∴ x = 24

⇒ Smaller number = 14x = 14 × 24 = 336

∴ The smaller of the two numbers is 336.

Given:

x : y = 6 : 5

And z : y = 9 : 25

Calculation :

x/y = 6/5     ---- (i)

And z/y = 9/25

⇒ y/z = 25/9     ---- (ii)

Multiply equation (i) and (ii) we get,

(x/y) × (y/z) = (6/5) × (25/9)

⇒ x/z = 10/3

∴ x : z = 10 : 3

Alternate Method 

x : y = 6 : 5     ----- (i)

And z : y = 9 : 25     ---- (ii)

As y is in both the ratios, Multiply (i) × 5 to make equal value of y in both the ratios

x : y = (6 : 5) × 5 = 30 : 25    ---- (iii)

from (ii) and (iii), Since y is same in both the ratios

x : z = 30 : 9 = 10 : 3
 

Given:

Ratio of Speed of Deepak and Vinod = 19 : 12

Let the speeds of Deepak and Vinod be 19x km/hr and 12x km/hr

Speed of Vinod = 84 km/hr

Calculations:

Speed of Vinod = 84 km/hr

⇒ 12x = 84

⇒ x = 7

Speed of Deepak = 19x = 19 × 7 = 133 km/hr

∴ The speed of Deepak is 133 km/hr.