Test: Ratio & Proportion - Grade 10 MCQ

Given:

The sum of 3 numbers is 285. Ratio between 2nd and 3rd numbers is 6 ∶ 5.

Ratio between 1st and 2nd numbers is 3 ∶ 7. 

Calculation:

Let the 1^st number be x 

Let the 2^nd number be y 

Let the 3^rd number be z 

The sum of 3^rd number is 285 

According to the question 

Ratio of 2^nd and 3^rd number 

⇒ y : z = 6 : 5 

Ratio of 1^th and 2^nd number 

⇒ x : y = 3 : 7 

Ratio of x : y : z 

⇒ (x × y) : (y × y) : (y × z) = (3 × 6) : (7 × 6) : (7 × 5)

⇒ x : y : z = 18 : 42 : 35

The 3^rd number z = 285 × 35 /(18 + 42 + 35) 

⇒ z = 285 × 35 / 95 = 105

∴   The 3rd number is 105

(108 + 36 + 72) ∶ (54 + 90)

= 216 ∶ 144

= 3 ∶ 2

Given :

Equation is a² + b² + c² - ab - bc - ca = 0

Solution :

Here we have 3 variables and only one equation .

Note  To solve these type of question we assume the value of any 2 variables.

Let assume that b = 1 and C = 1

⇒ a² + 1 + 1 - a - 1 - a = 0

⇒ a² + 1 - 2a = 0

⇒ ( a - 1 )² = 0  [ ∵  ( A+B )² = A² + B² + 2AB ]

Now a = 1

Now we have a = 1 , b = 1 and c = 1

So a : b : c = 1 : 1 : 1

Hence the correct answer is "1 : 1 : 1".

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 :

(i) a : b = 3 : 2,

(ii) b : c= 2 : 1,

(iii) c : d = 1/3 : 1/7,

(iv) d : e = 1/4 : 1/5

Calculations:

To solve these type of questions fill the blank by side values and then multiply all the ratios

Shortcut Trick:
a : b = 3 : 2 now check which options satisfied this ratio

1) a : b = 100 : 75 = 4 : 3 not equal to 3 : 2

2) a : b = 100 : 30 = 10 : 3 not equal to 3 : 2

3) a : b = 105 : 70 = 21 : 14 = 3 : 2 which is equal to 3 : 2

4) a : b = 105 : 35 = 21 : 7 = 3 : 1 which is not equal to 3 : 2

Hence option c is correct option

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

Formula Used: if u ∶ v = a ∶ b, then u × b = v × a.

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:

New ratio is 5 ∶ 2.

The price of diamond before broken is Rs. 12250.

Concept used:

Using the concept simple ratio.

Calculation:

Let the weight of each piece of diamond be 5x and 2x.

Total weight of diamond = 5x + 2x = 7x   

Cost of the diamond = (7x)² = 49x²

Cost of first piece = (5x)² = 25x²

Cost of second piece = (2x)² = 4x²

Total cost of diamond after weight = 25x² + 4x² = 29x² 

⇒ New cost = 29x² 

According to the question,

49x² = 12250

⇒ x² = 250

The loss in the price of diamond after broken = 49x² – 29x²

⇒ The required loss = 20x²

⇒ 250 × 20

⇒ Rs. 5000

∴ The loss in the price of diamond after broken is Rs. 5000.

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:

Total rupees = Rs 750 

Calculation:

A : B = 5 : 2 

B : C = 7 : 13 

A : B : C = 5 × 7 : 2 × 7 : 2 × 13 = 35 : 14 : 26 

Total Sum = 750 

⇒ 35 x + 14x + 26x = 750 

⇒ x = 10 

So, A's share = 35 × 10 = Rs 350 

∴ The required answer is Rs 350 

Given:

A - B = 3, B + C = 78, C + D = 33 and the average age of the family is 34 years

Formula used:

Total age = Average age × total number of peoples

Calculation:​

Total age of the family = 4 × 34 = 136 years

A + B + C + D = 136

⇒ A + B = 136 – 33     (∵ C + D = 33)

A + B = 103 years      ---- (i)

A – B = 3 years (Given)      ----- (ii)

From (i) and (ii)

2A = 106 years

∴ A = 53 years

B = 103 – 53 = 50 years    ( from i )

Also C + B = 78    (Given)

⇒ C = 78 – 50 = 28 years

∴ B – C = 50 – 28 = 22 years

Given:

Ratio of salaries of A and B = 5 : 6

New ratio = 11 : 13

Salary increment of each = Rs. 2000

Calculations:

Let the unit of ratio be x

A’s salary = 5x

B’s salary = 6x

After increment,

⇒ (5x + 2000)/(6x + 2000) = 11/13

⇒ 13(5x + 2000) = 11(6x + 2000)

⇒ 65x + 26000 = 66x + 22000

⇒ x = Rs. 4000

⇒ A’s new month salary = 5x + 2000 = 5 × 4000 + 2000

⇒ A’s new month salary = Rs. 22000

∴ The new monthly salary of A is Rs. 22000.

Given:

Total amount = Rs 1120

Ratio of coins of Rs 1, 50 paisa, and 25 paisa = 1 ∶ 1/2 ∶ 1/3

Formula Used:

Value of coins = Number of coins × per coin value

Calculation:

We know that

Rs 1 = 100 paisa

Ratio of value per coin = 100 ∶ 50 ∶ 25

⇒ 4 ∶ 2 ∶ 1

Ratio of number of coins = 1 ∶ 1/2 ∶ 1/3

⇒ 6 ∶ 3 ∶ 2

Total value of coins = 24 ∶ 6 ∶ 2

⇒ 12 ∶ 3 ∶ 1 = 16 units

⇒ 16 units = 1120

⇒ 1 units = 70

Value of 25 paisa coins = 1 units

⇒ 1 × 70

⇒ Rs. 70

∴ The total number of 25 paisa coins is Rs. 70.

Let the son’s ages be ‘x’ years and ‘y’ years

Given, x - y = 5

⇒ x = y + 5

Now,

Ratio of their shares = ratio of their ages

⇒ 54000 ∶ 48000 = x ∶ y

⇒ 9 ∶ 8 = (y + 5) ∶ y

⇒ 9y = 8y + 40

⇒ y = 40

∴ The younger son’s age is 40 years

Let the number of students in the classes be 2x, 3x and 4x respectively;
Total students = 2x + 3x + 4x = 9x
According to the question,

or, 24x + 96 = 22x + 132
or, 2x = 132 − 96 or,
x = 36/2 = 18
Hence,Original number of students,
9x = 9 × 18
= 162

Respective ratio of the Number of coins;
= 13 : 11 × 2 = 13 : 22
Hence, Number of 1 rupee coins;