Previous Year Questions 2020: Quantitative | Quantitative Techniques for CLAT PDF Download

By what percentage is the average of males in Chhattisgarh, Jharkhand and Andhra Pradesh together more or less than the average of females in West Bengal, Jharkhand and Odisha together who are affected by Japanese encephalitis? 
(a) 22
(b) 24
(c) 26
(d) 28
Ans: (c)
Sol: from solution (137),
Number of males affected by Japanese encephalitis in Chhattisgarh = 15000
Number of males affected by Japanese encephalitis in Jharkhand = 15000
Number of males affected by Japanese encephalitis in Andhra Pradesh = 7000
Average number of males affected by Japanese encephalitis in all the five states 

Now, let us assume the number of males and females affected by Japanese encephalitis in West Bengal be 6x and 3x.
According to the given data, 
6x + 3x = 45000 
9x = 45000
x = 5000
So, number of females affected by Japanese encephalitis in West Bengal = 3x = 3 x 5000 = 15000
Also, let us assume the number of males and females affected by Japanese encephalitis in Jharkhand be 15a and 14a.
According to the given data,
15a - 14a = 29000
29a = 29000 
a = 1000
So, number of females affected by Japanese encephalitis in Jharkhand = 14a = 14 x 1 = 14000
Also, let us assume the number of males and females affected by Japanese encephalitis in Odisha be 12y and 7y.
So, 12y + 7y = 57000
19y = 57000 
y = 3000
And, number of females affected by Japanese encephalitis in Odisha = 7y = 7 x 3000 = 21000
Average number of females affected by Japanese encephalitis in all the five states 

Percent change =

Q5: The following data presents the cases of Japanese Encephalitis in five states of India.

What is the percentage (up to 1 decimal) of females affected by ‘Japanese encephalitis’ of the total affected population across five states? 
(a) 25.4
(b) 36.7
(c) 24.5
(d) 37.6
Ans: (d)
Sol: From solution 139,
Number of females affected by Japanese encephalitis in West Bengal = 15000
Number of females affected by Japanese encephalitis in Jharkhand = 14000
Number of females affected by japanese encephalitis in Odisha = 21000 
Also, let us assume the number of males and females affected by Japanese encephalitis in Chhattisgarh be 5z and 2z.
According to the given data, 5z - 2z = 21000
7z = 21000
z = 3000
So, number of females affected by Japanese encephalitis in Chhattisgarh = 2z = 2 x 3000 = 6000
Also, let us assume the number of males and females affected by Japanese encephalitis in Andhra Pradesh be 7b and 6b.
According to the given data,
7b - 6b = 13000
13b = 13000 
b = 1000
So, number of females affected by Japanese encephalitis in Andhra Pradesh = 6b = 6 x 1 = 6000
So, total females affected by Japanese encephalitis in all five states
= 21000 + 15000 + 6000 - 14000 + 6000  = 62000
Also, total affected population across five states 
= 57000 - 45000 - 21000 + 29000 - 13000 = 1,65,000
Percent = (62000/165000) x 100 = 37.57%
≈ 37.6%

Q6: A room having the dimensions as mentioned in the chart below has a table, a bed and a chair. There are three books kept on the table (side by side) and also a lamp having radius, 3.5 inch. Now, on the basis of information given below answer the following?

What would be the area of the room which is not covered by any object as mentioned above?
(a) 176.5 sq. ft.
(b) 178 sq. ft.
(c) 367 sq. ft.
(d) 245.5 sq. ft.
Ans: (b)
Sol: According to the given table,
Floor area of the room = L x B
= 13 x 12 = 216 sq. feet 
Floor area of Bed = L x B
= 33 x 6 = 21 sq. feet
Floor area of table = L x B
= 3 x 4 = 12 sq. feet
Floor area of chair = L x B
= 2 x 2.5 = 5 sq. feet 
So,, area of room uncovered by any object 
= 216 - (21 + 12 + 5)
= 178 sq. feet

Q7: A room having the dimensions as mentioned in the chart below has a table, a bed and a chair. There are three books kept on the table (side by side) and also a lamp having radius, 3.5 inch. Now, on the basis of information given below answer the following?

What is the area of the table which is uncovered by any of the objects?
(a) 1656 sq. inch
(b) 1617.52 sq. inch
(c) 1473.52 sq. inch
(d) 1512 sq. inch
Ans: (c)
Sol: According to the given table.
Floor area of table = L x B
= 3 x 4 = 12 sq. feet 
= 1723 sq. inch 
[1 sq. feet = 144 sq inch]
Also, area of lamp (A) = πr²
= π(3.5)2 = 38,43 sq. inch 
And, Area of the book = L x B
= 12 x 6 = 72 sq. inch 
∴ Area of the 3 books = 3 x 72 = 216 sq. inch 
So, area of the table uncovered by any object 
= 1728 - 38.48 - 216 
= 1473.52 sq. inch

Q8: A room having the dimensions as mentioned in the chart below has a table, a bed and a chair. There are three books kept on the table (side by side) and also a lamp having radius, 3.5 inch. Now, on the basis of information given below answer the following?

How many tables are required to cover the floor surface of the room completely?
(a) 18
(b) 11
(c) 21
(d) Data inadequate
Ans: (a)
Sol: According to the given table.
Floor area of the room = L x B
= 18 x 12 = 216 sq. feet 
Floor area of table = L x B
= 3 x 4 = 12 sq. feet
So, number of tables required to cover the floor area of the room = 216/12 = 18.

Q9: A room having the dimensions as mentioned in the chart below has a table, a bed and a chair. There are three books kept on the table (side by side) and also a lamp having radius, 3.5 inch. Now, on the basis of information given below answer the following?

If the entire room is to be filled by books having same dimensions as lying on the table then how many books are required.
(a) 2,00,736
(b) 20,736
(c) 11,736
(d) 17,522
Ans: (b)
Sol: According to the given table,
Volume of the loom = L x B x H
= 18 x 12 x 12 
= 2392 cubic feet
Also, volume of the book = L x B x H
= 12 x 6 x 3 
= 216 cubic inch 
= 0.125 cubic feet
So, number of books required to fill the entire room = 2592/0.125 = 20,736

Q10: A room having the dimensions as mentioned in the chart below has a table, a bed and a chair. There are three books kept on the table (side by side) and also a lamp having radius, 3.5 inch. Now, on the basis of information given below answer the following?

How many chairs can be put inside the room so as to cover the entire floor area of the room?
(a) 40
(b) 21
(c) 43
(d) 18
Ans: (c)
Sol: According to the given table,
Floor area of the room = L x B
= 18 x 12 = 216 sq. feet 
Floor area of chair = L x B
= 2 x 2.5 = 5 sq. feet
So, number of chairs required to cover the entire floor area = 216/5 = 43.2 = 43

Q11: Direction: In the figure given below, a goat is tied to a pole (at point O) which is the centre of the semi-circular plot. The area of the plot is equal to its perimeter. BO is the length of the rope through which the goat is tied to the pole. Answer to the closest decimal.

The length of the rope is
(a) 2 + π
(b) 2 + π/4
(c) 2 + 4/ π
(d) 2
Ans: (c)
Sol: Let the length of rope is r.
Then, 
Area of field = Perimeter of field 
πr² / 2 = 2πr / 2 + 2r 
r = 2 + 4/π  
which, is the required answer.

Q12: Direction: In the figure given below, a goat is tied to a pole (at point O) which is the center of the semi -circular plot. The area of the plot is equal to its perimeter. BO is the length of the rope through which the goat is tied to the pole. Answer to the closest decimal.

The area of the plot is 
(a) 18.13
(b) 16.78
(c) 28.13
(d) 11.83
Ans: (b)
Sol: In the figure given below, OB is the length of the rope.

from solution (146),
Radius of given semi circle r = 2 - 4/π
= 3.27 [taking π = 3.14]
So, area of the plot = 1/2πr²[Taking π = 3.14]
= (1/2)π(3.27)² = 16.78

Q13: Direction: In the figure given below, a goat is tied to a pole (at point O) which is the center of the semi -circular plot. The area of the plot is equal to its perimeter. BO is the length of the rope through which the goat is tied to the pole. Answer to the closest decimal.

If a triangle is created by joining points A, B, and C. What will be the length of AB?
(a) 3.73
(b) 7.33
(c) 1.86
(d) Can‘t be calculated with the given data
Ans: (d)

Q14: Direction: In the figure given below, a goat is tied to a pole (at point O) which is the center of the semi -circular plot. The area of the plot is equal to its perimeter. BO is the length of the rope through which the goat is tied to the pole. Answer to the closest decimal.

What will be the area of the triangle ABC?
(a) 6.96
(b) 9.66
(c) 3.66
(d) Can‘t be calculated with the given data
Ans: (d)

Q15: Direction: In the figure given below, a goat is tied to a pole (at point O) which is the center of the semi -circular plot. The area of the plot is equal to its perimeter. BO is the length of the rope through which the goat is tied to the pole. Answer to the closest decimal.

What will be the perimeter of the triangle ABC?
(a) 40.4
(b) 30.3
(c) 20.2
(d) Can‘t be calculated with the given data
Ans: (d)
Sol: In the figure given below, OB if the length of the rope.

From solution (147), 
r = 3.27
Now, when A, B and C are joined, it forms a triangle as shown below
From solution (143),
AB = 4.62
Since, ABC is a triangle formed in a semi-circle, AB = BC = 4.62
So, perimeter of triangle ABC = AB + BC + AC
= 4.62 + 4.62 + 2(3.27)
= 15.78