3. AVERAGES EXERCISE Average
1.
Find the average of the first fifty natural numbers. a) 50 b) 51 c) 25 d) 25.5
2.
The average marks of 50 students in maths is 60 and the average marks of 50 students in science is 40. Find the average marks of all the 100 students. a) 25 b) 50 c) 40 d) 60
The average of ‘n’ quantities of the same kind, is represented as the ratio of the sum of all ‘n’ quantities to the total number of quantities.
Average =
Sumof Quantities
Totalnumberof Quantities Weighted Average of two groups If the average of ‘m’ quantities is ‘a’ and ‘n’ quantities 3. is ‘b’, then the average of the two groups is ma nb m n
Weighted Average of multiple groups
4.
Find the average of all odd numbers from 1 to 100. a) 25 b) 49 c) 50 d) 51
5.
The average of nine numbers is 40. If the average of the first five numbers is 38 and the last five is 43, find f ind the fifth number. a) 45 b) 55 c) 35 d) 25
6.
The average of five numbers is 27. If one of the numbers is excluded, the average becomes 25. Find the excluded number. a) 30 b) 35 c) 33 d) 34
7.
The average of 10 numbers is 7. If each number is multiplied by 8, the average of the new set of numbers is a) 48 b) 52 c) 54 d) 56
8.
The average monthly salary of 20 employees in an organization is Rs.2,000. If the manager’s salary is included, the average salary increases by Rs.200. What is the manager’s monthly salary? a) 2,600 b) 3,600 c) 6,200 d) 6,300
If the average of m 1 quantities is a 1 average of m 2 quantities is a 2 and so on until m n quantites, then the weighted average of the group is
m1a 1 m 2 a 2 m 3 a 3
............ m
The average weight of A, B and C is 50 kg. If the average weight of A & B is 45 kg and B & C is 48 kg, find the weight of B. a) 35 b) 40 c) 26 d) 36
n an
m1 m 2 ............. mn
9.
10.
11.
The average weight of the girls in a class is 17. The average of 5 two digit numbers increased 80 kg and that of the boys is 40 kg and the by 1.8 when one of the two digit number was overall average weight weight is 55 kg. If the number reversed. Find the original number. of girls in the class is 30, find the number of a) 32 b) 45 boys. c) 36 d) 79 a) 30 b) 40 18. If a, b, c, d and and e are five consecutive consecutive odd c) 50 d) 60 numbers, their average is If three numbers are in the ratio 4:5:6 and their average is 25, the largest number is a) 5(a + 4) b) abcde 5 a) 34 b) 36 c) 40 d) 30 c) 5(a +b + c + d + e) d) (a + 4) Of the three numbers, the first is twice the
19. If the average of a non-zero number and its
second and half the third. If the average of these three numbers is 56, the smallest number is a) 24 b) 22 c) 34 d) 32 th
12. A batsman scores 64 runs in the 16 inning which increases his average by 3. Find the average average after after the the 16 inning inning.. a) 18 c) 19
b) 17 d) 22
13. The average weight weight of 20 students in in a class is 40 kg. When a group of students with an average weight of 38 kg leaves the class, the average weight of the remaining students is increased by 0.5 kg. Find the number of students who left the class. a) 2 b) 4 c) 5 d) 8 14. Find the average average of the first 20 multiples multiples of 7. a) 75.3 b) 73.5 c) 735 d) 753 15.
The average of four consecutive even numbers is 27. Find the largest of these numbers.
a) 20 c) 27
b) 30 d) 24
16. If the average of a, b, c is M and ab+bc+ca=0, 2 2 2 the average of a , b and c is a) M b) 2M 2 2 c) 3M d) 4M
square is 5 times the number, find the number a) 9 b) 18 c) 27 d) 36 20. During an experiment, one observation was incorrectly read as 32 instead of 53 and the average of the 7 observations was 40. Find the actual average of all the 7 observations. a) 42 b) 43 c) 45 d) 52
EXERCISE
SIMPLE INTEREST & COMPOUND INTEREST
1
Simple Interest: Interest: Simple Interest is the interest calculated on the 2. original principal. The principal on which the interest is calculated remains constant throughout the time period. If P = Principal, R = Rate of interest per annum, T = Number of years,
Nilesh borrowed of Rs.20,000 at 20 % interest which is compounded annually.Find the total amount he needs to pay after 2 years. a) Rs.23,000 b) Rs.23,940 c) Rs.24,650 d) Rs.28,800
4.
A man borrowed Rs.8,000 at the rate of 12 % SI, and lent the same amount to another person at the rate of 15 %. W hat will be the gain after 7 years? a) Rs.1,300 b) Rs.1,450 c) Rs.1,680 d) Rs.1,720
A = Amount. then, SI =
and amount
100
P T R
A = P + SI = P +
TR = P 1
100
The difference between the compound interest and the simple interest on a sum of money borrowed at the rate of 20 % per annum for a period of 3 years is Rs.2,560. Find the amount borrowed. a) Rs.20,000 b) Rs.17,000 c) Rs.18,000 d) Rs.22,000
3.
SI = Simple Interest,
P T R
Calculate the SI on Rs.2,500 at the rate of 12 % per annum for 8 years. a) Rs.2,400 b) Rs.2,600 c) Rs.2,800 d) Rs.3,000
100
Compound Interest Compound interest is the interest added to the 5. principal at the end of each period and the amount thus obtained becomes the principal for the next period. If P = Principal,
A borrowed Rs.12,000 at the rate of 10 % and lent the same amount to B at the rate of 13 %. How much will A gain after 5 years? a) Rs.1,500 b) Rs.1,600 c) Rs.1,700 d) Rs.1,800
6.
The difference between the compound interest and the simple interest on a sum of money borrowed by Rajani at the rate of 30 % per annum for a period of 2 years is Rs.5,400. Find the amount borrowed. a) Rs.50,000 b) Rs.52,800 c) Rs.60,000 d) Rs.62,000
7.
A person borrowed Rs.30,000 at 20 % per annum compounded half yearly. What is the
R = Rate of interest per annuam, n = Number of years the principal is borrowed CI = Compound Interest, A = Amount.
R
then
n
compound interest for in 1½ year? a) Rs.9,930 b) Rs.9,856 c) Rs.6,487 d) Rs.8,745
P
CI =
100
p
R
1
100
TR and A =
100
n
n
1
8.
Vijay took a loan loan of Rs.25,000 for 5 years years at 15. SI. If the interest paid was Rs.12,500, what what is the rate of interest per annum? a) 10 % b) 11 % c) 12 % d) 13 %
A principal amounts amounts to Rs.8,880 in 4 years and Rs.9,600 in 5 years. What is the rate of interest? a) 8 % b) 10 % c) 12 % d) 14 %
9.
Venu borrowed a certain certain amount at 30 30 % per 16. If a certain sum of money triples in five years, annum compounded annually. annually. The final when compounded annually, in how many years will the sum become 81 times itself at amount paid by Venu in 2 years is Rs.50,700. Find the amount borrowed. the same rate of interest? a) Rs.30,250 b) Rs.32,250 a) 20 years b) 25 years c) Rs.31,200 d) Rs.30,000 c) 28 years d) 32 years
10.
Raj got a loan at 11% p.a. SI. After 5 years 17. If a sum of of money grows by five times when when he returned the principal along with the invested for 4 years in a scheme where interest. If he returns a total of Rs.12,400, w hat interest is compounded annually, how long will is the principal? the same sum of money grow by 625 times if a) Rs.6,000 b) Rs.7,000 invested at the same rate of interest when c) Rs.8,000 d) Rs.9,000 interest is compounded annually? a) 32 years b) 16 years Krishnan took a loan at 13 % p.a. SI. After 4 c) 64 years d) 125 years years he returned a total amount of Rs.9,120, what is the principal? 18. A principal amount earns earns Rs.12,000 as SI for a) Rs.6,000 b) Rs.7,000 7 years at the rate of 11 %. To get the same c) Rs.8,000 d) Rs.9,000 amount of interest in 11 years, what should be the rate of interest? Rs.700 amounts to Rs.16,800 in 5 years a) 6 % b) 7 % under SI. If the rate of interest is increased c) 8 % d) 9 % by 5 %, how much does it amount to? a) Rs.15,980 b) Rs.16,975 19. A gives Rs.1,500 to X for 4 years and Rs.2,500 c) Rs.17,540 d) Rs.18,450 to Y for 8 years. If the rate of interest is the same and if A receives Rs.2,080 from both X Rs.12,000 amounts to Rs.16,800 in 5 years. and Y, find the rate of interest. If the rate of interest is increased by 2 %, what a) 8 % b) 7 % would it amount to? c) 6 % d) 5 % a) Rs.15,000 b) Rs.16,975 c) Rs.17,000 d) Rs.18,000 20. Varshini gave Rs.30,000 Rs.30,000 to Suresh Suresh for 5 years years and Rs.20,000 to Vijay for 2½ years. If the In how many minimum integral years, will a rate of interest is the same and she receives certain amount of money double at 20 % Rs.14,000 SI from both, what is the rate of interest? compounded annually? a) 2 years b) 5 years a) 5 % b) 6 %
11.
12.
13.
14.
c) 4 years
d) 3 years
c) 7 %
d) 8 %
PROBLEMS ON AGES EXERCISE
The present ages of Sameer and Anand are in the ratio 5 : 4. Three years hence, the ratio of their ages will be 11: 9. What is Anand’s present age? a) 24 b) 27 c) 40 d) None of these
7.
2.
The present ages of A and B are in the ratio 5: 3. The ratio of A’s age 4 years ago and B’s age 4 years hence is 1 : 1. What is the ratio of A’s age 4 years hence and B’s age 4 years ago? a) 1 : 3 b) 2 : 1 c) 3 : 1 d) 4 : 1
8.
One year ago Pramila was four times as old as her daughter. Six years hence, Pramila’s age will exceed her daughter’s age by 9 years. The ratio of the present age of Pramila to that of her daughter is a) 12 : 7 b) 11 : 5 c) 13 : 4 d) 7 : 5
3.
The father’s age 10 years ago was thrice the age of his son. T en years hence, the father’s age will be twice that of his son’s. The ratio of their present ages is a) 5 : 2 b) 7 : 3 c) 9 : 2 d) 13 : 4
9.
At present, the ratio ratio of Arun’s and and Deepak’s Deepak’s age is 4: 3. After 6 years, Arun’s age Arun’s age will be 26 years. What is Deepak’s present age? a) 12 years b) 15 years c) 19 years d) 49 years
10.
The present ages of three persons are in the ratio 4:7:9. Eight years ago, the sum of their ages was 56. Find their present ages (in years). a) 8, 20, 28 b) 16, 28, 36 c) 20, 35, 45 d) None of these
11.
Half of Rohit’s age two years from now plus one-third of his age three years ago is twenty years. How old is he now? a) 24 b) 26 d) 16 c) 18
12.
The average age of five members of a family is 21 years. If the age of the grandfather is also included, the average increases by 9 years. The age of the grandfather is a) 75 b) 65 c) 45 d) 35
13.
Ramlal is four times as old as his son. Four years hence, the sum of their ages will be 43 years. The present age of the son is b) 6 a) 5
1.
4.
5.
6.
Rajan married 8 years ago. His present age is 6/5 times his age at the time of his marriage. If his sister was 10 years younger to him at the time of his marriage, find her present age a) 32 years b) 36 years c) 38 years d) 40 years Ayesha’s father’s age was 38 years when she was born. Her mother’s age was 36 years when, her brother who is four years younger to her was born. What is the difference between the ages of her parents? a) 2 years b) 4 years c) 6 years d) 8 years
The ages of Ram and Mukta are in the ratio 3 : 5. After 9 years the ratio of their ages will be 3 : 4. Find Mukta’s present age. a) 15 b) 20 c) 25 d) 30
Five years ago, the sum of the ages of a father and his son was 40 years and the ratio
of their present ages is 4:1. What is the present age of the father? a) 20 b) 30 d) 50 c) 40
14
Mrs. Malik is twice as old as her daughter Manu. Twenty years ago, the age of Mrs. Malik was 12 times Manu’s age. Find the present age of Mrs. Malik. a) 40 b) 44 c) 60 d) 50
15.
The average age of 10 boys in a hostel is 14. A new admission reduced the average age by one year. Find the age of the newly admitted boy. b) 5 a) 4 c) 12 d) 3
16.
The ratio of Lokesh’s age to that of his mother’s age is 4: 7. The difference in their ages is 33 years. Find the present age of Lokesh. a) 44 b) 33 c) 11 d) 30
17.
Treza is younger to Evelyne by as many years as she is older to Eileen. If the sum of the ages of Evelyne and Eileen is 80 years, how old is Treza? a) 64 b) 40 c) 32 d) 48
18.
A father’s age is is the reverse of his his son’s age. A year ago the father’s father’s age was was twice his son’s. What is the present age of the father? a) 89 b) 70 c) 73 d) 56
19.
One year ago, the ratio of Gaurav’s and Sachin’s ages was 6 : 7. Four years hence, the ratio would be 7 : 8. How old is Sachin now? a) 36 years b) 35 years c) 34 years d) 32 years
20.
Jyothi’s age was thrice Kiran’s age, when Jyothi was as at of Kiran’s present age. If the sum of their present ages is 80 years, find the present age of Kiran. a) 30 b) 50 c) 40 d) 20
