1. The average of 5 nos. is 46 and that of the first four of them is 45. The fifth number is
Sol:
The fifth number = total of 5 numbers  total of first four numbers
= 5 X 46  4 X 45
= 230  180 = 50
The 5th number is 50.
2. The average of n numbers is x.When 36 is substracted from two of the numbers, the new average becomes (x8). The value of n is
Sol:
The average of ‘n’ numbers = x
Total of ‘n’ numbers = nx
According to this question,
nx – 3636 = n(x8)
nx – 72 = nx8n
8n = 72
N = 72/8 = 9
The value of n is 9.
3. Four years ago the average age of A, B and C was 25 years. Five years ago the average age of and C was 20 years. A’s present ages is
Sol:
Four years ago,
Average of A+B+C = 25 years
Now the age of A+B+C = 3 X 25 + 12 = 75 + 112 = 87 years.
Five years ago,
Average of B+C = 20 years
Now, the age of B+C = 2 X 20 + 10 = 40 + 10 = 50 years
A’s present age = (A+B+C) is present ages – (B+C) is present ages
= 87 – 50 = 37 years.
4. A person goes to a place at the speed of 20 km/hr and returns at the speed of 12 km/hr. His average speed for the journey is
Sol:
Average speed = (2xy/x+y) km/hr.
X = 20km/hr. Y = 12 km/hr.
Average speed = 2 X 200 X 12 / 20 + 12
= 2 X 20 X 12 / 32
= 15 km/hr.
5. The average age of 20 boys in a class is 12 years. What will be the average age of the class of 5 new boys take admission whose average age is 7 years?
Sol:
Total ages of 20 boys = 20 X 12 = 240 years
Total ages of 5 new boys = 5 X 7 = 35 years
In the class, 25 boys total ages = 240 + 35 = 275 years
Average age of 25 boys = 275/25 = 11 years
7  3  4 
5  6  ? 
2  8  3 
33  10  33 
6. ? = 9
Sol:
7 X 5 = 35 – 2 = 33
6 X 3 = 18 – 10 = 8
4 X 9 = 36 – 3 = 33
5 
 7 
 99 

4 
 3 
3 
 9 
 ? 

7 
 5 
7 
 6 
 114 

5 
 2 
2.
? = 164
Sol:
5 square = 25
7 square = 49
4 square = 16
3 square = 9
So total = 99 same for the another two also.
8. If x = 8 + 2√15, the value of √x + 1/√x is
Sol: X = 8 + 2√15
2 2
= (√5) + (√3) + 2√5 √3
2
= (√5 + √3)
√x = √5 + √3 and 1/√x
= 1/√5 + √3 X √5  √3 / √5  √3
= √5  √3 / 2
√x + 1/ √x = √5 + √3 + √5  √3 / 2
= 2√5 + 2√3 + √5  √3 / 2
= 3√5 / 2 + √3 /2
9. A boy walked 3 km towards south. Then he turned towards west and walked for 5 km. Then he turned towards north and walked for 6 km. Now he turned towards east and walked for 5 km.
What is the distance between the boy and the starting point?
Sol : 3 kms.
10. The ratio of the velocities of the hour hand and the minute hand of a clock is
Sol:
Velocity = distance / time
Velocity of hour hand / Velocity of minute hand
= 360 / 12 X 60 = 360 X 60 / 360 X 12 X 60 = ½
360 / 60
 UPSC Maths Study Materials
 HISTORY OF INDIA UPSC STUDY MATERIALS
 SSC study materials – Computer
 SSC study materials – History
 general intelligence and reasoning for upsc exams
 upsc exam  study materials  history
 upsc exam  study materials  maths
 materials for upsc exam  history
 UPSC Chemistry Exam Study Materials
 Chemistry Study Materials for UPSC Exam 3
 Chemistry Study Materials for UPSC Exam 2
 Chemistry Study Materials for UPSC Exam 1
0 comments:
Please post your thoughts and queries for UPSC Maths Study Materials