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

Given:

(m + n) : (m - n) = 7 : 3

Concept Used:

Componendo and Dividendo 

If a/b = c/d 

then (a + b)/(a - b) = (c + d)/(c - d)

Or, (a - b)/(a + b) = (c - d)/(c + d)

Calculation:

(m + n)/(m - n) = 7/3

On applying componendo and dividendo, we get 

[(m + n) + (m - n)]/[(m + n) - (m - n)] = [7 + 3]/[7 - 3]

⇒ m/n = 5/2

On squaring both side, we get 

⇒ m²/n² = 25/4

Again apply componendo and dividendo, we get 

(m2 - n²)/(m2 + n2) = (25 - 4)/ (25 + 4)

∴ The value of (m2 - n2) : (m2 + n2) is 21 : 29.

Given:

Sum of two parts = 141

One-eighth part of the first part and one-ninth part of the second part are in the ratio 5:6.

Calculation:

Let the first part be x and the second part be (141 - x).

According to the given condition:

Cross multiplying gives:

⇒ 9x / 8 × 6 = 5(141 - x)

⇒ 54x / 8 = 705 - 5x

⇒ 54x = 5640 - 40x

⇒ 94x = 5640

⇒ x = 60

The first part is 60.

Given:

Total Income = ₹6,00,000

Number of children = 4

Eldest son: share

Second son: share

Third son: share

Formula used:

Total shares = Sum of individual shares

Share of fourth son = Total Income - Sum of shares of first three sons

Calculations:

Step 1: Calculate share of eldest son.

Share of eldest son = = ₹1,00,000

Step 2: Calculate share of second son.

Share of second son = = ₹1,50,000

Step 3: Calculate share of third son.

Share of third son = = ₹3,00,000

Step 4: Calculate sum of shares.

Sum of shares = ₹1,00,000 + ₹1,50,000 + ₹3,00,000 = ₹5,50,000

Step 5: Calculate share of fourth son.

Share of fourth son = ₹6,00,000 - ₹5,50,000 = ₹50,000

Answer:

The fourth son will get ₹50,000.

Given:

Income ratio of P and Q = 5:4

Expenditure ratio of P and Q = 4:3

Savings of P is more than that of Q by 16²/₃%

Formula used:

Income = Savings + Expenditure

Savings difference = ^{(Savings of P - Savings of Q)}/Savings of Q × 100

Percentage of income spent = ^Expenditure/Income × 100

Calculations:

Let the income of P and Q be 5x and 4x respectively.

Let the expenditure of P and Q be 4y and 3y respectively.

Savings of P = Income of P - Expenditure of P = 5x - 4y

Savings of Q = Income of Q - Expenditure of Q = 4x - 3y

Given: Savings difference = 16²/₃%

16²/₃% = 50/3%

⇒ ^{(5x - 4y - (4x - 3y))}/ (4x - 3y) × 100 = 50/3

⇒ ^{x - y}/(4x - 3y) × 100 = 50/3

⇒ (x - y)/(4x - 3y) = 1/6

⇒ 6(x - y) = 4x - 3y

⇒ 6x - 6y = 4x - 3y

⇒ 2x = 3y

⇒ y = 2x/3

Percentage of income spent by P:

⇒ ^{Expenditure of P}/Income of P × 100 = ^4y/5x × 100

⇒ ^4(2x/3)/5x × 100

⇒ ^8x/15x × 100

⇒ 800/15

⇒ 53¹/₃%

∴ The correct answer is option (3).

Given:

P : Q : R = 2 : 3 : 4

P² + Q² + R² = 11600

Formula used:

Let P = 2k, Q = 3k, R = 4k

P² + Q² + R² = (2k)² + (3k)² + (4k)²

Calculation:

(2k)² + (3k)² + (4k)² = 11600

⇒ 4k² + 9k² + 16k² = 11600

⇒ 29k² = 11600

⇒ k² = 11600 ÷ 29

⇒ k² = 400

⇒ k = √400

⇒ k = 20

P = 2k = 2 × 20 = 40

Q = 3k = 3 × 20 = 60

R = 4k = 4 × 20 = 80

P + Q - R = 40 + 60 - 80

⇒ P + Q - R = 20

∴ The correct answer is option 1.

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:

Ratio of salaries of A and B = 6 : 7

B's salary increased by 

Total salary of B = Rs. 147700

Calculation:

Let salary of A and B be Rs. 60x and Rs. 70x

Now,

Increased salary of B = 70x + 70x × 

⇒ Rs. 73.85x

According to the question,

73.85x = 147700

⇒ x = 147700/73.85

⇒ x = 2000

So, actual salary of A = 60 × 2000

⇒ Rs. 120000

∴ The salary (in Rs.) of A is 120000.

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