Exercise : 1


1. The average of two numbers is XY. If one number is X, then the other number is
(a) Y
(b) Y2
(c) 2XY – X
(d) X(Y – 1)
(e) None of these
Ans.c

Let the other number is N.

Then , \(\frac{X + N}{2}\) = XY ⇒ N = 2XY - X

2. The average of four consecutive odd numbers is 12. Which is the lowest odd number?
(a) 9
(b) 3
(c) 5
(d) Cannot be determined
(e) None of these
Ans.a

Let the four consecutive odd nos. be

2x – 3, 2x – 1, 2x + 1 and 2x + 3.

Now, 2x = 12 or, x = 6

Lowest odd no. = 2 × 6 – 3 = 9

3. The average marks scored by Ganesh in English, Science, Mathematics and History is less than 15 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography scored by him?
(a) 40
(b) 50
(c) 60
(d) Data inadequate
(e) None of these
Ans.c

\(\frac{E + H + G + M}{4} \; - \; \frac{E + S + M + H}{4} = 15\)

⇒ G - S = 60

4. The average age of 24 students and the class teacher is 16 years. If the class teacher’s age is excluded, the average reduces by one year. What is the age of the class teacher?
(a) 50 years
(b) 45 years
(c) 40 years
(d) Data inadequate
(e) None of these
Ans.c

Age of the CT = 25 × 16 – 24 × 15 = 400 – 360 = 40 yrs.

5. There are 50 boys in a class. Their average weight is 45 kg. When one boy leaves the class, the average reduces by 100 g. Find the weight of the boy who left the class.
(a) 40.9 kg
(b) 42.9 kg
(c) 49.9 kg
(d) 39.9 kg
Ans.c

Here one boy is excluded and final average of the group decreases.

∴ change in average is (–)ve = – 0.1 kg.

Using the formula

Sum of the quantities excluded

= \(\begin{pmatrix} Change \; in \; no. \; of \; quantities\\ \times \\ Original \; Average\end{pmatrix} + \begin{pmatrix} Change \; in \; Average\\ \times \\ Final \; no. \; of \; quantities\end{pmatrix}\)

⇒ weight of the boy who left = (1 × 45) – (– 0.1 × 49)

= 49.9 kg

∴ weight of the boy who left the class is 49.9 kg.

6. The average age of 36 students in a group is 14 years. When teacher’s age is included to it, the average increases by one. What is the teacher’s age in years?
(a) 31
(b) 36
(c) 51
(d) cannot be determined
Ans.c

Age of the teacher = (37 × 15 – 36 × 14) years

= 51 years.

7. The average weight of 8 persons increases by 1.5 kg. If a person weighing 65 kg is replaced by a new person, what could be the weight of the new person?
(a) 76 kg
(b) 77 kg
(c) 76.5 kg
(d) Data inadequate
(e) None of these
Ans.b

total weight increases = 8 × 1.5 = 12 kg

so the weight of new person = 65 + 12 = 77 kg

8. N number of persons decide to raise 3 lakhs by equal contributions from each. If they contributed 50 each extra, the contribution would be 3.25 lakhs. How many persons are there?
(a) 600
(b) 400
(c) 450
(d) Cannot be determined
(e) None of these
Ans.e

Required persons = \(\frac{325000 - 300000}{50}\) = 500

9. The average of the first and the second of three numbers is 15 more than the average of the second and the third of these numbers. What is the difference between the first and the third of these three numbers?
(a) 15
(b) 45
(c) 60
(d) Data inadequate
(e) None of these
Ans.e

Set the first, second and third no be F, S and T

Respectively \(\frac{F + S}{2} = \frac{S + T}{2} + 15\). Solving, we get F – T = 30.

10. The average of Suresh’s marks in English and History is 55. His average of marks in English and Science is 65. What is the difference between the marks which he obtained in History and Science?
(a) 40
(b) 60
(c) 20
(d) Data inadequate
(e) None of the above
Ans.c

E + H = (55 × 2) = 110;

E + S = (65 × 2) = 130

∴ Reqd difference = 130 – 110 = 20