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

Given:

Mean proportion = 68

x = Unknown

Second term = 272

Formula used:

If 68 is the mean proportion between x and 272, the formula used is:

Mean proportion = √(x × 272)

Calculation:

68 = √(x × 272)

⇒ 68² = x × 272

⇒ 4624 = x × 272

⇒ x = 4624 ÷ 272

⇒ x = 17

∴ The correct answer is option (1).

Given:

Ratios to compare:

41 : 64, 50 : 59, 40 : 70, 26 : 90

Formula used:

Convert each ratio to decimal:

Calculations:

∴ The greatest ratio is 50 : 59.

Given:

Ratio of red to green tokens = 7:20

Ratio of pink to red tokens = 15:12

Formula Used:

To find the ratio of green to pink tokens, we align the ratios using the common term "red".

Calculation:

Ratio of red to green tokens = 7:20

Ratio of pink to red tokens = 15:12

First, express the ratios in terms of a common "red" count:

Let red tokens = 84 (LCM of 7 and 12)

Green tokens = (20 × 84) / 7 = 240

Pink tokens = (15 × 84) / 12 = 105

Now, find the ratio of green to pink tokens:

Green : Pink = 240 : 105

Simplify the ratio:

⇒ Green : Pink = (240 / 15) : (105 / 15)

⇒ Green : Pink = 16 : 7

The ratio of green to pink tokens is 16:7.

Given:

Calculations:

⇒ = = 69.6

∴ The corrcetv ansrwt is option 3.

Given:

x : y = 2 : 5

y : z = 4 : 7

Total Amount = ₹15,120

Formula used:

To combine two ratios, we use the Least Common Multiple (LCM) of the common term (y).

Final Ratio (x : y : z) = x : y : z after adjustment.

Distribution = Total Amount × (Individual ratio / Sum of all ratios)

Calculation:

x : y = 2 : 5, y : z = 4 : 7

x : y = 8 : 20, y : z = 20 : 35

⇒ Combined Ratio (x : y : z) = 8 : 20 : 35

Sum of Ratios = 8 + 20 + 35 = 63

Amount for x = ₹15,120 × (8 / 63)

⇒ Amount for x = ₹1920

Amount for y = ₹15,120 × (20 / 63)

⇒ Amount for y = ₹4800

Amount for z = ₹15,120 × (35 / 63)

⇒ Amount for z = ₹8400

∴ The amounts received by x, y, and z are ₹1920, ₹4800, and ₹8400 respectively.

The correct answer is option (2).

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:

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 : 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:

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,  = (5/4)/(4/5) = 25/16

∴  = 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:

The ratio of the salaries of Ravi and Sarita is 3 ∶ 5.

If the salary of each is increased by ₹ 5,000, the new ratio becomes 29 ∶ 45.

Formula Used:

Initial salaries: R = 3x and S = 5x.

New salaries: R + 5000 and S + 5000.

New ratio: (R + 5000) / (S + 5000) = 29/45.

Calculation:

Substituting the values of R and S in the new ratio equation:

(3x + 5000) / (5x + 5000) = 29 / 45

Cross multiplying to solve for x:

⇒ 45 × (3x + 5000) = 29 × (5x + 5000)

⇒ 135x + 225000 = 145x + 145000

⇒ 145x - 135x = 225000 - 145000

⇒ 10x = 80000

⇒ x = 8000

Now, finding the current salary of Sarita:

S = 5x = 5 × 8000

S = 40000

The present salary of Sarita is ₹ 40,000.

Shortcut Trick 

Let my current age = x years and my cousin’s age = y years.

Three-fifths of my current age is the same as five-sixths of that of one of my cousins’,

⇒ 3x/5 = 5y/6

⇒ 18x = 25y

My age ten years ago will be his age four years hence,

⇒ x – 10 = y + 4

⇒ y = x – 14,

⇒ 18x = 25(x – 14)

⇒ 18x = 25x – 350

⇒ 7x = 350

∴ x = 50 years