Surds and Indices Aptitude Questions and Answers – Quantitative Aptitude

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 Pn. Here, P is called the base and n is known as the index of the power.

  • am * an = am+n
  • (am / an) = am-n
  • (am)n = amn
  • (ab)n = anbn
  • (a / b)n = (an / bn)
  • a0 = 1
  • a-m = (1 / am)
  • If an, then m = n

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

Time and Work

Question 1
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
A
12 days
B
15 days
C
16 days
D
18 days
Question 1 Explanation: 
Answer: Option B
Explanation:
Question 2
P can complete a work in 12 days working 8hrs a day. Q can complete the same work in 8days working 10hrs a day. If both P and Q work together, working 8hrs a day, in how many days can they complete the work?
A
60/11
B
61/11
C
71/11
D
72/11
Question 2 Explanation: 
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
A man can repair a road in 7hrs. How many men are required to repair the road in 2hrs?
A
17 men
B
14 men
C
13 men
D
16 men
Question 3 Explanation: 
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
4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
A
35
B
40
C
45
D
50
Question 4 Explanation: 
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
Dev Completed the school project in 20days. How many days will Arun take to complete the same work if he is 25% more efficient then dev?
A
10 days
B
12 days
C
16 days
D
15 days
Question 5 Explanation: 
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
A can fabricate a divider in 30 days, while B alone can assemble it in 40 days, if they construct it together and get an installment of Rs. 7000, What B's offer?
A
2000
B
3000
C
4000
D
6500
Question 6 Explanation: 
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
A works twice as fast as B. If B can complete a work in 18 days independently, the number of days in which A and B can together finish the work is:
A
4 days
B
6 days
C
8 days
D
10 days
Question 7 Explanation: 
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
A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:
A
4 days
B
6 days
C
8 days
D
12 days
Question 8 Explanation: 
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
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, They completed the work in 3 days. How much is to be paid to C?
A
Rs. 375
B
Rs. 400
C
Rs. 600
D
Rs. 800
Question 9 Explanation: 
Answer: Option B
Explanation:
Question 10
The rates of working of A and B are in the proportion 3:4. The No. Of days taken by them to complete the work is in the proportion.
A
3 : 4
B
9 : 16
C
4 : 3
D
2 : 4
Question 10 Explanation: 
Answer: Option C
Explanation:
Ratio of time taken = (1/3 : 1/4) = 4 :3
There are 10 questions to complete.
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