- Maths Inequalities Quiz 17
- Maths Inequalities Quiz 16
- Maths Inequalities Quiz 15
- Maths Inequalities Quiz 14
- Maths Inequalities Quiz 13
- Maths Inequalities Quiz 12
- Maths Inequalities Quiz 11
- Maths Inequalities Quiz 10
- Maths Inequalities Quiz 9
- Maths Inequalities Quiz 8
- Maths Inequalities Quiz 7
- Maths Inequalities Quiz 6
- Maths inequalities Quiz 5
- Maths inequalities Quiz 4
- Maths Inequalities Quiz 3
- Maths Inequalities Quiz 2
- Maths Inequalities Quiz 1

Important for :

1

C

Let the length of the train be ‘x’ m

So, the speed of the train = | x |

8 |

Also, the speed of train = | x + 330 |

23 |

So, | x | = | x + 330 |

8 | 23 |

23x = 8x + 2640

15x = 2640; x = 176

So, the speed of the train = | 176 | = 22 m/s = 79.2 km/h |

8 |

Let the original average speed of the car be ‘x’ km/h

According to the question,

180 | – | 180 | = | 9 |

x – 5 | x | 60 |

x

x

x (x – 80) + 75(x – 80) = 0

(x – 80)(x + 75) = 0

x = 80, – 75

Speed can’t be negative. So, the value of ‘x’ = 80

So, the original average speed of the car = 80 km/hr

So, Quantity I < Quantity II

So option (C) is the correct answer.

2

A

Let the capacity of the tank = 200 litres (LCM of 20, 25 and 40)

Quantity of water filled by pipe A alone in one hour

= | 200 | = 10 litres |

20 |

Quantity of water filled by pipe B alone in one hour

= | 200 | = 8 litres |

25 |

Quantity of water emptied by pipe C alone in one hour

= | 200 | = 5 litres |

40 |

Quantity of water filled by pipe A alone in five hours = 10 × 5 = 50 litres

Quantity of water filled by pipe A and B together in 4 hour = (10 + 8) × 4 = 72 litres

Quantity of remaining water to be filled by pipes A, B and C together = 200 – 50 – 72 = 78 litres

Time taken by pipes A, B and C together to fill the remaining 78 litres

= | 78 | = | 78 | = 6 hours |

10 + 8 – 5 | 13 |

So, total time taken to fill the empty tank = (5 + 4 + 6) = 15 hours

Let the time taken by B alone to complete the work be ‘x’ hours

So, the time taken by A alone to complete the work

= | x | = | 2x | hours |

1.5 | 3 |

So, according to question,

1 | + | 3 | x = | 1 |

x | 2 | 6 |

5x | = | 1 | ; x = 15 |

2 | 6 |

So, time taken by A alone to complete the work

= | 15 | = 10 hours |

1.5 |

So, Quantity I > Quantity II

So option (A) is the correct answer.

3

A

213

Number |
Divisor |
Remainder |

213^{16} |
17 | 1 |

213^{1} |
17 | 9 |

213^{2} |
17 | -4 |

213^{4} |
17 | -1 |

213^{8} |
17 | 1 |

213^{15} |
17 | 2 |

Unit digit of (any odd number except 5 at unit’s place)

Therefore, unit digit of

So, Quantity I > Quantity II

So option A is the correct answer.

4

C

Let the monthly income of Shukla be Rs. ‘100x’

So, amount spends by Shukla on EMI = 0.24×100x=Rs.24x

So, amount spends by Shukla on children’s education = 0.12×100x=Rs.12x

So, remaining income = (100x – 24x – 12x) = Rs.64x

So, the amount spends by Shukla on Investment and Entertainment = (0.20 + 0.05) × 64x = Rs.16x

Therefore, savings = (64x – 16x) = 48x

According to question,

48x = 21600 ; x = 45

So, income of Shukla = 100x = 45000

Therefore, the amount spends by Shukla on Entertainment = 0.05 × 64 × 450 = Rs.1440

Let, the income of Raju and Vinesh be Rs. ‘4x’ and Rs.‘3x’ respectively

According to the question,

(4x – 10000)/(3x – 6000) = 5/4

16x – 40000 = 15x – 30000

x = 10000

So, the income of Vinesh = 3 × 10000 = 30000

Therefore, the amount is given to sister by Vinesh = 0.05 × 30000 = Rs.1500

So, Quantity I < Quantity II

So option (C) is the correct answer.

5

E

Let, speed of Sanju, Sanjay and Shailesh be ‘A’ m/s, ‘B’ m/s, ‘C’ m/s respectively.

According to question,

560 | = | 560 – 80 |

A | B |

560 | = | 480 |

A | B |

A | = | 7 |

B | 6 |

Also,

440 | = | 440 – 110 |

A | C |

440 | = | 330 |

A | C |

C | = | 3 |

A | 4 |

Using both the equations, we get

A : B : C = 28 : 24 : 21

Ratio of the speed of Sanju: Sanjay: Shailesh = 28 : 24 : 21

Distance run by Sanjay = 480 m

Distance run by Shailesh = | 480 | × 21 = 420 m |

24 |

So, Sanjay will beat Shailesh by (480 – 420) = 60m

Let, side of square garden be ‘x’ m

So, length of rectangular garden = 1.5x m

So, breadth of rectangular garden = 1.125m

According to the question,

x

x

2.6875x

x^{2} = |
4300 |

2.6875 |

x

x = 40 m

Therefore, length of rectangular park = 1.5 × 40 = 60m

So, Quantity I = Quantity II or No relation

So, option (E) is the correct answer.