# CAT Linear Equations Questions

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CAT Linear Equations Questions consists of important linear equations questions for CAT. This CAT questions will help in solving quantitative aptitude questions in CAT.

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CAT Linear Equations Questions:

Question 1:

I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more what I had paid. What per cent of the total amount paid by me was paid for the pens?

A. 37.5%

B. 62.5%

C. 50%

D. None of these

Question 2:

Out of two-thirds of the total number of basketball matches, a team has won 17 matches and lost 3 of them. What is the maximum number of matches that the team can lose and still win more than three- fourths of the total number of matches, if it is true that no match can end in a tie?

A. 4

B. 6

C. 5

D. 3

Question 3:

A piece of string is 40 cm long. It is cut into three pieces. The longest piece is three times as long as the middle-sized and the shortest piece is 23 cm shorter than the longest piece. Find the length of the shortest piece.

A. 27

B. 5

C. 4

D. 9

Question 4:

Mayank, Mirza, Little and Jaspal bought a motorbike for $60. Mayank paid one-half of the sum of the amounts paid by the other boys. Mirza paid one-third of the sum of the amounts paid by the other boys. Little paid one-fourth of the sum of the amounts paid by the other boys. How much did Jaspal have to pay? A.$15

B. $13 C.$17

D. None of these

Question 5:

Two full tanks, one shaped like a cylinder and the other like a cone, contain jet fuel. The cylindrical tank holds 500 litres more than the conical tank. After 200 litres of fuel has been pumped out from each tank the cylindrical tank contains twice the amount of fuel in the conical tank. How many litres of fuel did the cylindrical tank have when it was full?

A. 700

B. 1000

C. 1100

D. 1200

Answer and Solutions for CAT Linear Equations Questions:

Let the cost of pen, pencil and eraer be x,y,z respectively
5x+7y+4z = A
6x+8z+14y = 3A/2
4x + 16/3 z + 28/3 y = A
Comparing two equations
5x+7y+4z = 4x+16/3 z + 28/3 y
x = 7/3 y + 4/3 z
3x = 7y+4z
Now required percentage = $$\frac{5x}{5x+7y+4z}*100 = \frac{5x}{5x+3x} = 62.5%$$

Total matches played = 17+3 = 20
Total matches = 20*$$\frac{3}{2}$$ = 30
Number of wins required = 75% of 30 = 22.5 = 23 wins
23-17 = 6 more wins are required out of 10 matches to maintain 75% win recor which means there would be 4 losses.

Let the longest piece be x
Shortest piece = x – 23
Middle-sized piece = x/3
So, x + x – 23 + x/3 = 40 => 7x/3 = 63 => x = 27
Shortest piece = 27 – 23 = 4

Let the amount paid by Mayank be x. So, amount paid by the other three = 2x
=> Total bill = x+2x = 3x = 60 => x = 20. So, Mayank paid 20
Similarly, amount paid by Mirza + 3*Amount paid by Mirza = 60
=> Amount paid by Mirza = 15
Amount paid by Little + 4*Amount paid by Little = 60
=> Amount paid by Little = 12
So, amount paid by Jaspal = 60 – (20+15+12) = 60 – 47 = \$13