**Surds and Indices** Aptitude Questions and Answers – Formulas & Tricks

**Surds:**

Let a be rational Number and n be a positive integer, Such that a^{(1/n)} = ^{n}√a, Then, ^{n}√a is called a surd of order n.

Numbers which can be expressed in the form √p + √q, Where P and Q are natural number and not perfect squares. Irrational number which contain the radical sign (n√) are called as surds. Hence, the numbers in the form of √3, ^{3}√2, ….. ^{n}√x

**Laws of Surds**

**Indices:**

When a number P is multiplied by itself n times, then the product is called n th power of P and is written as P^{n}. Here, P is called the base and n is known as the index of the power.

- a
^{m}* a^{n}= a^{m+n} - (a
^{m}/ a^{n}) = a^{m-n} - (a
^{m})^{n}= a^{mn} - (ab)
^{n}= a^{n}b^{n} - (a / b)
^{n}= (a^{n}/ b^{n}) - a
^{0}= 1 - a
^{-m}= (1 / a^{m}) - If a
^{n}, then m = n

Surds and Indices Aptitude Questions and Answers With Detailed Explanation – Quantitative Aptitude

## Time and Work

Question 1 |

12 days | |

15 days | |

16 days | |

18 days |

**Answer: Option B**

__Explanation:__

Question 2 |

60/11 | |

61/11 | |

71/11 | |

72/11 |

**Answer: Option A**

__Explanation:__

P can complete the work in (12 * 8)hrs = 96hrs

Q can complete the work in (8 * 10)hrs = 80hrs

Therefore, P's 1 hrs work = 1/96 and Q's 1hrs work = 1/80

(P+Q)'s 1hrs work = ( 1/96) + (1/80) = 11/480. So both P and Q will finish the work in 480/11hrs

Therefore, No.of Days of 8hrs each = (480/11) * (1/8) = 60/11

Question 3 |

17 men | |

14 men | |

13 men | |

16 men |

**Answer: Option B**

__Explanation:__

M * T / W = Comstant

Where, M = Men

T = Time Taken

W = Work Load

So, here we apply

M1 * T1 / W1 = M2 * T2 / W2

Given, M1 = 4men, T1 = 7hrs , T2 = 2hrs, We have to find M2 = ?

Note, that here, W1 = W2 = 1 road, ie. equal work load

Clearly, Substituting in the above equation we get, M2 = 14 men.

Question 4 |

35 | |

40 | |

45 | |

50 |

**Answer: Option B**

__Explanation:__

Let 1 man's 1 day's work = x and 1 women's 1 day's work = y

Then 4x + 6y = (1/8) and 3x + 7y =(1/10)

Solving the two equation, We get x= (11/400), y = (1/400)

Therefore, 1 women's 1 day's work = (1/400)

10 women's 1 day's work = (1/400) * 10 = (1/40)

Hence, 10 women will complete the work in 40 days.

Question 5 |

10 days | |

12 days | |

16 days | |

15 days |

**Answer: Option C**

__Explanation:__

Let the days taken by Arun to complete the work be x

The ratio of time taken by Arun and Dev = 125:100 = 5:4

5:4 ::20:x

x = (( 4 * 20 ) / 5)

**x = 16**

Question 6 |

2000 | |

3000 | |

4000 | |

6500 |

**Answer: Option B**

__Explanation:__

A's 1 days work = 1/30,

B's 1 day work = 1/40,

Proportion of their shares = (1/30) : (1/40) = 4 : 3

B's offer = (7000 * (3/7)) =Rs. 3000

Question 7 |

4 days | |

6 days | |

8 days | |

10 days |

**Answer: Option B**

__Explanation:__

Ratio of rates of working of A and B = 2 : 1.

So, ratio of times taken = 1 : 2

Therefore, A's 1 day's work = 1/9

B's 1 day's work = 1/8

(A+B)'s 1 day's work = (1/9) + (1/8) = (1/6)

So, A and B together can finish the work in 6 days

Question 8 |

4 days | |

6 days | |

8 days | |

12 days |

**Answer: Option B**

__Explanation:__

Suppose A, B and C take x, (x/2), and (x/3) days respectively to finish the work.

Then, ((1/x) + ( 2/x) + (3/x)) = 1/2

=> (6/x) = (1/2)

=> x = 12

So, B takes (12/2) = 6 days to finish the work.

Question 9 |

Rs. 375 | |

Rs. 400 | |

Rs. 600 | |

Rs. 800 |

**Answer: Option B**

__Explanation:__

Question 10 |

3 : 4 | |

9 : 16 | |

4 : 3 | |

2 : 4 |

**Answer: Option C**

__Explanation:__

Ratio of time taken = (1/3 : 1/4) = 4 :3