Class 9 Maths: Data | Practice Extra Questions

Ans: C

Explanation: To find the average, sum the populations and divide by the number of cities (5). 74 + 64 + 15 + 21 + 70 = 244. 244 / 5 = 48.8

Ans: D

We can let n = the number of students and x = the average age of the students. So we have:

(30 + x + nx)/(n + 1) = x + 1.5

30 + x + nx = (x + 1.5)(n + 1)

30 + x + nx = nx + x + 1.5n + 1.5

30 = 1.5n + 1.5

1.5n = 28.5

n = 19

Ans: D

Let, the ratio is K:1

SO, Copper : Zinc = 8k+2 : k+7

Now,

8k+2/k+7= k/1

solve for k, k=2

so the ratio is k:1=2:1

Ans: D

The total score of the original 30 students is 30×75 = 2250.
Let the score of the new student be y.
The new average for 31 students is:
(2250+y)/31 = 76
Multiplying both sides by 31 gives:
2250+y = 2356
y = 106.

Ans: B

According to the question,
6T + 12C = 7800
Average price of table = Rs. 750
Total price of tables= 750 × 6 = Rs. 4500
Total price of chairs= 7800 – 4500 = Rs. 3300
Average price of chairs= $\frac{3300}{12}$ = Rs. 275

Ans: B

1. Let ‘x’ kg of Rs. 15 per kg wheat be mixed with ‘y’ kg of Rs. 18 per kg wheat.
2. The total cost of ‘x’ kg of Rs. 15 wheat = 15x
3. The total cost of ‘y’ kg of Rs. 18 wheat = 18y
4. The total cost of the mixture = 15x + 18y
5. The total weight of the mixture = x + y
6. The cost of the mixture per kg = (15x + 18y) / (x + y)
7. Given the mixture is worth Rs. 17 per kg: (15x + 18y) / (x + y) = 17
8. Solve for the ratio x/y:
15x + 18y = 17x + 17y
y = 2x
9. Therefore, x/y = 1/2
10. The ratio of the Rs. 15 per kg wheat to Rs. 18 per kg wheat is 1:2

Ans: D

Calculation
= 3276 divided by 4550, multiplied by 100
= 18 divided by 25, multiplied by 100
= 72 percent
The result is 72%

Ans: B

Three identical vessels in the ratio 4:1, 5:2 and 6 :1 respectively.
Petrol : kerosene
(4 : 1 = 5)7
(5 : 2 = 7)5
(6 : 1 = 7)5
28 : 7 = 35
25 : 10 = 35
30 : 5 = 35
83 : 22

Ans: B

1. Calculate the cost price of the mixture: Selling price – Profit = 20 – 2 = 18 Rs/kg
2. Apply the alligation rule: (Superior wheat price – Mixture price) : (Mixture price – Inferior wheat price) = Ratio of quantities
3. Substitute the values: (28 – 18) : (18 – 14)
4. Simplify: 10 : 4
5. Reduce the ratio: 5 : 2

Ans: A

Efficient Approach

Let the initial total volume of the mixture be represented by 16x.
The initial proportions are: Orange = 5x, Apple = 7x.

When 24 litres of the mixture are removed, the quantities of each component taken out are:
Orange removed = (5 / 16) * 24 = 7.5 litres
Apple removed = (7 / 16) * 24 = 10.5 litres

The difference between the resultant Apple and Orange volumes is given as 14 litres.
Resultant Apple volume = Initial Apple volume – Apple removed
Resultant Orange volume = Initial Orange volume – Orange removed + Orange added (which is 10L in the alternate method but the first method implies a net addition/removal)

The provided equation from the original explanation is:
(7x − 10.5) − (5x − 7.5 + 10) = 14
This simplifies to:
2x − 13 = 14
2x = 27

The initial total quantity is 16x.
Initial quantity = 16 * (27/2) = 216 litres.
Therefore, the correct answer is 216 litres.

Alternative Approach

Given information:
Ratio of Orange : Apple : Guava = 5 : 7 : 4
Volume of mixture extracted = 24 litres
Volume of juices added = 10 litres Orange, 6 litres Guava
Final difference between Apple and Orange juice = 14 litres

Calculations:
Total ratio parts initially = 5 + 7 + 4 = 16 parts
Let the initial total quantity of the mixture be 16x litres.
The initial volumes are: Orange = 5x, Apple = 7x, Guava = 4x.

Volume of Orange juice extracted = (5 / 16) * 24 = 7.5 litres
Volume of Apple juice extracted = (7 / 16) * 24 = 10.5 litres

After removing 24 litres and adding the specified juices, the new volumes are:
Resultant Orange juice = 5x – 7.5 + 10 = 5x + 2.5 litres
Resultant Apple juice = 7x – 10.5 litres

According to the problem statement, the difference is 14 litres:
(7x – 10.5) – (5x + 2.5) = 14
7x – 10.5 – 5x – 2.5 = 14
2x – 13 = 14
2x = 27
x = 13.5

The initial quantity of the mixture = 16x = 16 * 13.5 = 216 litres.
Thus, the correct answer is 216 litres.

Supplementary Concepts

Constant Ratio Principle
When a portion of a mixture is removed, the remaining mixture maintains the original proportions of its components. Altering these proportions solely occurs when individual components are selectively added or removed.

Replacement Method
When a specific volume of a mixture is entirely substituted with one of its pure constituents, the remaining quantity of that pure constituent can be determined using the formula:
Final Quantity = Initial Quantity * (1 – (Volume Removed / Total Volume))^n
where ‘n’ is the number of replacement cycles.

Alligation Rule
This method is utilized to determine the required ratio when two ingredients with differing values or concentrations are combined. The ratio is calculated as:
Ratio = (Higher Value – Mean Value) : (Mean Value – Lower Value)

Ans: D

Calculation:
Observation 1:
Amount of rice cultivated by Entity A during 2016 = 50 lakh metric tons
Amount of rice cultivated by Entity C during 2020 = 45 lakh metric tons
Observation 1 is not accurate.
Observation 2:
Amount of rice cultivated by Entity B during 2018 = 50 lakh metric tons
Amount of rice cultivated by Entity A during 2018 = 55 lakh metric tons
Amount of rice cultivated by Entity C during 2018 = 60 lakh metric tons
Observation 2 is not accurate.
Observation 3:
Total rice cultivation in 2017 = 40 + 60 + 50 = 150 lakh metric tons
Total rice cultivation in 2018 = 55 + 50 + 60 = 165 lakh metric tons
Observation 3 is not accurate.
Observation 4:
Amount of rice cultivated by Entity B during 2017 = 60 lakh metric tons
Amount of rice cultivated by Entity A during 2020 = 60 lakh metric tons
Observation 4 is accurate.
Therefore, the correct choice is 4.

Ans: C

Going by relation of mixtures

We know that

4(0.40) + 5 (x%) = 9 (0.50)

or, 5(x%) = 9(0.50)-4(0.40)

or, x% =2.9/ 5 = 0.58

ie x= 58 %

Ans: D

Now, w:m :: 9:15 L

Lt x L water be added

5:3 :: (9+x):15

x=16 L

Ans: C

Explanation: Let the money Pankaj has be x. Soham has 50% more than Pankaj, so Soham has 1.5x. Mukesh has twice as much as Soham, so Mukesh has 2 * 1.5x = 3x. The average money they have is Rs. 110, so (x + 1.5x + 3x) / 3 = 110. This simplifies to 5.5x / 3 = 110. Therefore, 5.5x = 330, and x = 60. Mukesh has 3x, so Mukesh has 3 * 60 = 180.

Ans: B

Explanation: Let the weight of Bhavya be x kg. Then the weight of Chinu is 3x kg and the weight of Arshi is 2x kg. The average weight of the 3 children is 20 kg, so their total weight is 3 * 20 = 60 kg. Therefore, x + 3x + 2x = 60. Simplifying gives 6x = 60, so x = 10 kg. The weight of Chinu is 3x = 3 * 10 = 30 kg.

Ans: C

To solve this problem, we first need to figure out the proportion of red paint in the original Perfect Pink mixture and then use that to scale up to the desired 34 pints.

From the problem, we know:

– 3/4 pint of red paint is used

– 2/3 pint of white paint is used

Total pints of Perfect Pink paint in the original mix are:

$ \frac{3}{4} + \frac{2}{3} $

We need a common denominator to add these fractions, which would be 12:

$ \frac{3 \times 3}{4 \times 3} + \frac{2 \times 4}{3 \times 4} = \frac{9}{12} + \frac{8}{12} = \frac{17}{12} \text{ pints of Perfect Pink} $

Now, we calculate the proportion of red paint in the mix:

$ \text{Proportion of red paint} = \frac{\text{Quantity of red paint}}{\text{Total quantity of paint mix}} = \frac{3/4}{17/12} $

To simplify:

$ \frac{3/4}{17/12} = \frac{3/4 \times 12/17} = \frac{3 \times 12}{4 \times 17} = \frac{36}{68} = \frac{18}{34} = \frac{9}{17} $

Thus, 9/17 of the Perfect Pink mix is red paint.

Now, we are asked to find the amount of red paint needed for 34 pints of Perfect Pink paint. We calculate:

$ \frac{9}{17} \times 34 \text{ pints} = 9 \times 2 = 18 \text{ pints of red paint} $

Therefore, 18 pints of red paint are needed to make 34 pints of Perfect Pink paint.

Ans: A

In order to find equal quantities to be mixed, we’ll need to find equivalent ratios such that the SUMS of the terms are equal.

Take the ratio

and multiply all terms by

to get the equivalent ratio:

Notice that

So, in

units of the first mixture, there are

units of petrol,

units of diesel and

units of kerosene.

Similarly,

units of the second mixture, there are

units of petrol,

units of diesel and

units of kerosene.

When we combine

units of each mixture, we get 28 units in the ratio: (

+

) : (

+

) : (

+

), which simplifies to be