Simple Ratios MCQ Quiz - Objective Question with Answer for Simple Ratios - Download Free PDF

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.

Calculation:

Total students = x + 25

Girls = 2/3 of boys

Let boys = b, then girls = (2/3)b

⇒ Total = b + (2/3)b = (5/3)b

⇒ (5/3)b = x + 25 ⇒ b = (3/5)(x + 25)

Now: Boys (P : NP) = 3:1 ⇒ Non-participating boys = 1/4 of b = b/4

Girls (P : NP) = 3:1 ⇒ Non-participating girls = 1/4 of (2/3)b = (1/6)b

Total non-participating = b/4 + b/6 = (5/12)b

Given: (5/12)b = 35 ⇒ b = (35 × 12)/5 = 84

Total = (5/3) × 84 = 140

x + 25 = 140 ⇒ x = 115

∴ The value of x is 115.

Given:

Ratio of A to B = 8 : 11

A = 168

Calculation:

A / B = 8 / 11

168 / B = 8 / 11

168 × 11 = 8 × B

1848 = 8B

B = 1848 / 8

B = 231

∴ The value of B is: 231

Given:

Ratio of boys to girls = 5:3

After 10 boys leave, ratio becomes = 1:1

Formula used:

Let the number of boys = 5x

Let the number of girls = 3x

Total people = Boys + Girls

After 10 boys leave:

Remaining boys = 5x - 10

Remaining girls = 3x

New ratio = Remaining boys : Remaining girls = 1 : 1

Calculation:

Given new ratio:

(5x - 10) / 3x = 1/1

⇒ 5x - 10 = 3x

⇒ 5x - 3x = 10

⇒ 2x = 10

⇒ x = 5

Total boys = 5x = 5 × 5 = 25

Total girls = 3x = 3 × 5 = 15

Total people = Boys + Girls = 25 + 15 = 40

∴ The correct answer is option (2).

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 

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: 

5p : 10p : 25p = 3 : 2 : 1 = 3x : 2x : x

Concept:

1 Rupee = 100 paise

Calculation:

60 Rupees = 60 × 100 = 6000 paise

⇒ 5 × 3x + 10 × 2x + 25 × 1x = 6000

⇒ 15x + 20x + 25x = 6000

⇒ 60x = 6000

⇒ x = 100

∴ Number of 5 paise coins = 3x = 3 × 100 = 300

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.

Shortcut Trick

P : Q : R = 5 : 3 : 6

Le P be 5x, Q be 3x and R be 6x

Then, (P/Q) ∶ (Q/R) ∶ (R/P) = (5x/3x) ∶ (3x/6x) ∶ (6x/5x)

Let us take the LCM (3, 6, 5) = 30

So, (P/Q) ∶ (Q/R) ∶ (R/P) = (5x/3x) × 30 ∶ (3x/6x) × 30 ∶ (6x/5x) × 30

∴ Required ratio is 50 ∶ 15 ∶ 36

Alternate Method

Given:

P : Q : R = 5 : 3 : 6

Le P be 5x, Q be 3x and R be 6x.

Concept:

If N is divided into a : b, then

First part = N × a/(a + b)

Second part = N × b/(a + b)

Calculations:

The required ratio = P/Q : Q/R : R/P

Multiplying the above ratio with PQR

⇒ Required ratio = P²R : Q²P : R²Q

Putting values of P,Q and R in above ratio, we get

⇒ Required ratio = (5x)²(6x) : (3x)²(5x) : (6x)²(3x)

⇒ Required ratio = (25x²)(6x) : (9x²)(5x): (36x²)(3x)

⇒ Required ratio = (25)(2) : (3)5: (36)

⇒ Required ratio = 50 : 15 : 36

∴ Required ratio is 50 ∶ 15 ∶ 36.

Given:

Total Rs. = Rs.550

Calculation:

Let the number of denominations of 50p = 2x

the number of denominations of 25p = 3x

the number of denominations of 20p = 5x

Total paisa = 550 × 100 = 55000 paise

According to the question:

⇒ (50 × 2x) + (25 × 3x) + (20 × 5x) = 55000

⇒ 100x + 75x + 100x = 55000

⇒ 275x = 55000

⇒ x = 55000/275 = 200

Amount in (Rs.) of 50p = 100x = (100 × 200) = 20000 paise = Rs.200

Amount in (Rs.) of 20p = 100x = (100 × 200) = 20000 paise = Rs.200

Required difference = 200 - 200 = 0

∴ The correct answer is 0.