Quantitative Aptitude – Geometry – Mensuration – A solid metallic cube

Quantitative Aptitude – Geometry – Mensuration

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Geometry - Mensuration - A solid metallic cube
A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1 : 1 : 8: 27: 27. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to

A) 10
B) 50
C) 60
D) 20

Answer

Option (B)

Solution

As per the question from CAT 2017 – Quantitative Aptitude – Geometry – Mensuration,
Ratio of volumes of 5 smaller cubes and original big one = 1 : 1 : 8 : 27 : 27 : 64
Ratio of sides = 1 : 1 : 2 : 3 : 3 : 4
Ratio of areas = 1 : 1 : 4 : 9 : 9 : 16
The sum of the areas of the 5 smaller cubes is 24 parts while that of the big cube is 16 parts. The sum is 50% greater.
Option (B)

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CAT 2017 Questions from Quantitative Aptitude – Geometry

Quantitative Aptitude – Geometry – Mensuration – Q1: The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length.
Quantitative Aptitude – Geometry – Mensuration – Q2: A ball of diameter 4 cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is 3 cm, while its volume is 9 π cm^3 .
Quantitative Aptitude – Geometry – Coordinate – Q1: The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is
Quantitative Aptitude – Geometry – Coordinate – Q2: The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length.
Quantitative Aptitude – Geometry – Circles – Q1: ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120 degrees and ∠BAC = 30 degrees, then the value of ∠BCD (in degrees) is
Quantitative Aptitude – Geometry – Circles – Q2: Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC.
Quantitative Aptitude – Geometry – Triangles – Q1: Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB.
Quantitative Aptitude – Geometry – Triangles – Q2: Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km, respectively.
Quantitative Aptitude – Geometry – Triangles – Q3: From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. The area, in sq ft, of the remaining portion of triangle ABC is
Quantitative Aptitude – Geometry – Polygons – Ques: Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is

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Quantitative Aptitude – Geometry – Circles – Let ABC be a right-angled isosceles

Quantitative Aptitude – Geometry – Triangles

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Geometry - Circles - Let ABC be a right-angled isosceles
Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC. Let BPC be an arc of a circle centered at A and lying between BC and BQC. If AB has length 6 cm then the area, in sq cm, of the region enclosed by BPC and BQC is

A) 9π – 18
B) 18
C) 9π
D) 9

Answer

Option (B)

Solution

As per the question from CAT 2017 – Quantitative Aptitude – Geometry – Circles,
Quantitative Aptitude - Geometry - Circles - Let ABC be a right-angled isosceles
Let AB = a (a = 6)
CQB is a semicircle of radius a/√2
CPB is a quarter circle (quadrant) of radius a
So, area of semicircle = pi*a^2/4
Area of quadrant = pi*a^2/4
So, area of region enclosed by BPC, BQC = Area of tr(ABC) = 18.
Option (B)

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Geometry

Quantitative Aptitude – Geometry – Circles – Ques: ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120 degrees and ∠BAC = 30 degrees, then the value of ∠BCD (in degrees) is
Quantitative Aptitude – Geometry – Triangles – Q1: Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB.
Quantitative Aptitude – Geometry – Triangles – Q2: Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km, respectively.
Quantitative Aptitude – Geometry – Triangles – Q3: From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. The area, in sq ft, of the remaining portion of triangle ABC is
Quantitative Aptitude – Geometry – Coordinate – Q1: The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is
Quantitative Aptitude – Geometry – Coordinate – Q2: The shortest distance of the point (½, 1) from the curve y = |x -1| + |x + 1| is
Quantitative Aptitude – Geometry – Mensuration
Quantitative Aptitude – Geometry – Polygons – Ques: Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is

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​​

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Quantitative Aptitude – Geometry – Triangles – From a triangle ABC with sides

Quantitative Aptitude – Geometry – Triangles

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Geometry - Triangles - From a triangle ABC with sides
From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. The area, in sq ft, of the remaining portion of triangle ABC is

A) 225√3
B) 500 / √3
C) 275 / √3
D) 250 / √3

Answer

Option (B)

Solution

As per the question from CAT 2017 – Quantitative Aptitude – Geometry – Triangles,
Area of triangle = root (s(s-a)(s-b)(s-c))
S = 50
Area = 250 * root(3)
Centroid divides triangle in the ratio 2:1
Area of remaining portion of triangle: 2/3 * (Area of Triangle) = 500/root(3)
Option (B)

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Geometry

Quantitative Aptitude – Geometry – Triangles – Q1: Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB.
Quantitative Aptitude – Geometry – Triangles – Q2: Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km, respectively.
Quantitative Aptitude – Geometry – Circles – Q1: ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120 degrees and ∠BAC = 30 degrees, then the value of ∠BCD (in degrees) is
Quantitative Aptitude – Geometry – Circles – Q2: Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC.
Quantitative Aptitude – Geometry – Coordinate – Q1: The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is
Quantitative Aptitude – Geometry – Coordinate – Q2: The shortest distance of the point (½, 1) from the curve y = |x -1| + |x + 1| is
Quantitative Aptitude – Geometry – Mensuration
Quantitative Aptitude – Geometry – Polygons – Ques: Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is

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Quantitative Aptitude – Algebra – Functions – The area of the closed region

Quantitative Aptitude – Algebra – Functions

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Algebra - Functions - The area of the closed region
The area of the closed region bounded by the equation | x | + | y | = 2 in the two-dimensional plane is

A) 4π
B) 4
C) 8
D) 2π

Answer

Option (C)

Solution

As per the question from CAT 2017 – Quantitative Aptitude – Algebra – Functions,
Remember the formula |x| + |y| = n
Here, area bounded by the region = 2n^2
In the question, n=2
So, area = 8
Option (C)

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Algebra – Functions

Quantitative Aptitude – Algebra – Functions – Q1: Let f(x) = 2x-5 and g(x) = 7-2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if
Quantitative Aptitude – Algebra – Functions – Q2: If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is
Quantitative Aptitude – Algebra – Functions – Q3: Let f(x) = x^2 and g(x) = 2^x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is
Quantitative Aptitude – Algebra – Functions – Q4: If f(x) = (5x+2)/(3x-5) and g(x) = x^2 – 2x – 1, then the value of g(f(f(3))) is
Quantitative Aptitude – Algebra – Functions – Q5: If f1(x) = x^2 + 11x + n and f2(x) = x, then the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots, is
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Quantitative Aptitude – Arithmetic – Averages – A class consists of 20 boys

Quantitative Aptitude – Arithmetic – Averages

Question

CAT 2017 - Forenoon slot -Quantitative Aptitude - Arithmetic - Averages - A class consists of 20 boys
A class consists of 20 boys and 30 girls. In the mid-semester examination, the average score of the girls was 5 higher than that of the boys. In the final exam, however, the average score of the girls dropped by 3 while the average score of the entire class increased by 2. The increase in the average score of the boys is

A) 9.5
B) 10
C) 4.5
D) 6

Answer

Option (A)

Solution

As per CAT 2017 – Quantitative Aptitude – Arithmetic – Averages, we can see that
Score of girls = x
Score of boys = y
As per the question, x/30 = y/20 + 5
Average of class = (x + y)/ 50
New score of girls = x’
New score of boys = y’
x/30 – 3 = x’/30
(x’ + y’)/50 = (x + y)/50 + 2
x’ = x – 90
On solving we get, y’ = y + 190
New average of boys = (y + 190)/20 = y/20 + 9.5
So, average of boys increases by 9.5
Option (A)

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Arithmetic

Quantitative Aptitude – Arithmetic – Averages – Ques: The average height of 22 toddlers increases by 2 inches when two of them leave this group.
Quantitative Aptitude – Arithmetic – Mixtures – Q1 : Consider three mixtures – the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1 : 3, and the third having water and liquid C in the ratio 1 : 4.
Quantitative Aptitude – Arithmetic – Mixtures – Q2: Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water in 9 : 4 ratio.
Quantitative Aptitude – Arithmetic – Time and Work – Q1: Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 days and are paid a total amount of Rs 1000 as remuneration.
Quantitative Aptitude – Arithmetic – Time and Work – Q2: A person can complete a job in 120 days. He works alone on Day 1. On Day 2, he is joined by another person who also can complete the job in exactly 120 days.
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Quantitative Aptitude – Algebra – Simple Equations – If a and b are integers

Quantitative Aptitude – Algebra – Simple Equations

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Algebra - Simple Equations - If a and b are integers
If a and b are integers of opposite signs such that (a + 3)^2 : b^2 = 9 : 1 and (a – 1)^2 : (b – 1)^2 = 4 : 1, then the ratio a^2 : b^2 is

A) 9:4 ‘
B) 81:4
C) 1: 4
D) 25: 4

Answer

Option (D)

Solution

As per the question from CAT 2017 – Quantitative Aptitude – Algebra – Simple Equations,

We get 4 cases
CASE – 1
a+3 = 3b
a-1 = 2b-2

CASE – 2
a+3 = 3b
a-1 = 2b + 2

CASE – 3

a+3 = -3b
a-1 = 2b-2

CASE – 4
a+3 = -3b
a-1 = -2b+2

Subtracting the second equation from the first we get,
Case 1: 4 = b+2 => b = 2, a = 3 (Rejected as a and b should be of opposite sign)

Case 2: 4 = b-2 => b = 6, a = 15 (Rejected as a and b should be of opposite sign)

Case 3: 4 = -5b+2 => b = -2/5 (Rejected as both a and b are integers)

Case 4: 4 = -b-2 => b = -6, a = 15 (Accepted)

So, a^2/b^2 = (15/6)^2 = 25/4
Option (D)

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CAT 2017 Questions from Quantitative Aptitude – Algebra

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Quantitative Aptitude – Arithmetic – Profit and Loss – If Fatima sells 60 identical toys

Quantitative Aptitude – Arithmetic – Profit and Loss

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Arithmetic - Profit and Loss - If Fatima sells 60 identical toys
If Fatima sells 60 identical toys at a 40% discount on the printed price, then she makes 20% profit. Ten of these toys are destroyed in fire. While selling the rest, how much discount should be given on the printed price so that she can make the same amount of profit?

A) 30%
B) 25%
C) 24%
D) 28%

Answer

Option (D)

Solution

As per CAT 2017 – Quantitative Aptitude – Arithmetic – Profit and Loss, we can see that
Market Price = MP
Cost Price = CP
[(60/100 MP * 60 – 60CP)/60CP] * 100 = 20
MP = 2CP
When 10 toys are burnt in fire, then
[(x/100 *50 * MP – 60CP )/60CP] * 100 = 20
x = 72
So discount given = 100-72 = 28%
Option (D)

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Arithmetic

Quantitative Aptitude – Arithmetic – Profit and Loss – Q1: Mayank buys some candies for Rs 15 a dozen and an equal number of different candies for Rs 12 a dozen.
Quantitative Aptitude – Arithmetic – Profit and Loss – Q2: The manufacturer of a table sells it to a wholesale dealer at a profit of 10%. The wholesale dealer sells the table to a retailer at a profit of 30%.
Quantitative Aptitude – Arithmetic – Profit and Loss – Q3: In a market, the price of medium quality mangoes is half that of good mangoes.
Quantitative Aptitude – Arithmetic – Profit and Loss – Q4: If a seller gives a discount of 15% on retail price, she still makes a profit of 2%. Which of the following ensures that she makes a profit of 20%?
Quantitative Aptitude – Arithmetic – Mixtures – Q1 : Consider three mixtures – the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1 : 3, and the third having water and liquid C in the ratio 1 : 4.
Quantitative Aptitude – Arithmetic – Mixtures – Q2: Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water in 9 : 4 ratio.
Quantitative Aptitude – Arithmetic – Time and Work – Q1: Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 days and are paid a total amount of Rs 1000 as remuneration.
Quantitative Aptitude – Arithmetic – Time and Work – Q2: A person can complete a job in 120 days. He works alone on Day 1. On Day 2, he is joined by another person who also can complete the job in exactly 120 days.
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Quantitative Aptitude – Arithmetic – Profit and Loss – In a market, the price of medium quality

Quantitative Aptitude – Arithmetic – Profit and Loss

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Arithmetic - Profit and Loss - In a market, the price of medium quality
In a market, the price of medium quality mangoes is half that of good mangoes. A shopkeeper buys 80 kg good mangoes and 40 kg medium quality mangoes from the market and then sells all these at a common price which is 10% less than the price at which he bought the good ones. His overall profit is

A) 6%
B) 8%
C) 10%
D) 12%

Answer

Option (B)

Solution

As per CAT 2017 – Quantitative Aptitude – Arithmetic – Profit and Loss, we can see that
Price of good Quality mangoes = p
Price of medium Quality mangoes = p/2
Price at which mangoes are sold = 0.9p
Profit = [( 0.9p * 120 – 100p)/100p] * 100 = 8%
Option (B)

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Arithmetic

Quantitative Aptitude – Arithmetic – Profit and Loss – Q1: Mayank buys some candies for Rs 15 a dozen and an equal number of different candies for Rs 12 a dozen.
Quantitative Aptitude – Arithmetic – Profit and Loss – Q2: The manufacturer of a table sells it to a wholesale dealer at a profit of 10%. The wholesale dealer sells the table to a retailer at a profit of 30%.
Quantitative Aptitude – Arithmetic – Profit and Loss – Q3: If Fatima sells 60 identical toys at a 40% discount on the printed price, then she makes 20% profit.
Quantitative Aptitude – Arithmetic – Profit and Loss – Q4: If a seller gives a discount of 15% on retail price, she still makes a profit of 2%. Which of the following ensures that she makes a profit of 20%?
Quantitative Aptitude – Arithmetic – Mixtures – Q1 : Consider three mixtures – the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1 : 3, and the third having water and liquid C in the ratio 1 : 4.
Quantitative Aptitude – Arithmetic – Mixtures – Q2: Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water in 9 : 4 ratio.
Quantitative Aptitude – Arithmetic – Time and Work – Q1: Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 days and are paid a total amount of Rs 1000 as remuneration.
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Quantitative Aptitude – Arithmetic – Ratios – A stall sells popcorn and chips

Quantitative Aptitude – Arithmetic – Ratios

Question

CAT 2017 - Forenoon slot -Quantitative Aptitude - Arithmetic - Ratios - A stall sells popcorn and chips
A stall sells popcorn and chips in packets of three sizes: large, super, and jumbo. The numbers of large, super, and jumbo packets in its stock are in the ratio 7 : 17 : 16 for popcorn and 6 : 15 : 14 for chips. If the total number of popcorn packets in its stock is the same as that of chips packets, then the numbers of jumbo popcorn packets and jumbo chips packets are in the ratio

A) 1: 1
B) 8: 7
C) 4: 3
D) 6: 5

Answer

Option (A)

Solution

As per CAT 2017 – Quantitative Aptitude – Arithmetic – Ratios, we can see that
Total no of popcorn = 40x
Total no of chips = 35y
40x = 35y
x/y = 7/8
Jumbo popcorn = 16x
Jumbo chips = 14y
Ratio = 16x/14y
Putting values of x and y, we get 1:1 as answer
Option (A)

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Arithmetic

Quantitative Aptitude – Arithmetic – Ratios – Ques: Suppose, C1, C2, C3, C4, and C5 are five companies. The profits made by C1, C2, and C3 are in the ratio 9 : 10 : 8 while the profits made by C2, C4, and C5 are in the ratio 18 : 19 : 20.
Quantitative Aptitude – Arithmetic – Mixtures – Q1 : Consider three mixtures – the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1 : 3, and the third having water and liquid C in the ratio 1 : 4.
Quantitative Aptitude – Arithmetic – Mixtures – Q2: Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water in 9 : 4 ratio.
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Quantitative Aptitude – Arithmetic – Percentages – The number of girls appearing

Quantitative Aptitude – Arithmetic – Percentages

Question

CAT 2017 - Forenoon slot -Quantitative Aptitude - Arithmetic - Percentages - The number of girls appearing
The number of girls appearing for an admission test is twice the number of boys. If 30% of the girls and 45% of the boys get admission, the percentage of candidates who do not get admission is

A) 35
B) 50
C) 60
D) 65

Answer

Option (D)

Solution

As per CAT 2017 – Quantitative Aptitude – Arithmetic – Percentages, we can see that
No of girls = g
No of boys = b
g = 2b
No of girls who do not get admission = 0.7g = 1.4b
No of boys who do not get admission = 0.55b
% = [(1.4b + 0.55b)/3b] * 100 = 65%
Option (D)

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Arithmetic

Quantitative Aptitude – Arithmetic – Percentages – Q1: In a village, the production of food grains increased by 40% and the per capita production of food grains increased by 27% during a certain period.
Quantitative Aptitude – Arithmetic – Percentages – Q2: Out of the shirts produced in a factory, 15% are defective, while 20% of the rest are sold in the domestic market. If the remaining 8840 shirts are left for export, then the number of shirts produced in the factory is
Quantitative Aptitude – Arithmetic – Percentages – Q3: Ravi invests 50% of his monthly savings in fixed deposits. Thirty percent of the rest of hi√√s savings is invested in stocks and the rest goes into Ravi’s savings bank account.
Quantitative Aptitude – Arithmetic – Mixtures – Q1 : Consider three mixtures – the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1 : 3, and the third having water and liquid C in the ratio 1 : 4.
Quantitative Aptitude – Arithmetic – Mixtures – Q2: Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water in 9 : 4 ratio.
Quantitative Aptitude – Arithmetic – Time and Work – Q1: Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 days and are paid a total amount of Rs 1000 as remuneration.
Quantitative Aptitude – Arithmetic – Time and Work – Q2: A person can complete a job in 120 days. He works alone on Day 1. On Day 2, he is joined by another person who also can complete the job in exactly 120 days.
Quantitative Aptitude – Arithmetic – Time, Speed and Distance
Quantitative Aptitude – Arithmetic – Profit and Loss
Quantitative Aptitude – Arithmetic – Pipes and Cisterns – Ques: A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in 8 hours.
Quantitative Aptitude – Arithmetic – Averages
Quantitative Aptitude – Arithmetic – Ratios

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