Exercise : 2


1. The average of four consecutive even numbers is one-fourth of the sum of these numbers. What is the difference between the first and the last number?
(a) 4
(b) 6
(c) 2
(d) Cannot be determined
(e) None of these
Ans.b

Let the four consecutive even nos. be 2x, 2x + 2, 2x + 4 and 2x + 6 respectively.

Reqd difference = 2x + 6 – 2x = 6

2. The average of three consecutive odd numbers is 14 more than one-third of the first of these numbers, what is the last of these numbers?
(a) 17
(b) 19
(c) 15
(d) Data inadequate
(e) None of these
Ans.d

Let the three consecutive odd numbers be

x – 2, x, x + 2 respectively.

According to question,

\(x = \frac{x - 2}{3} + 14\)

∴ 3x – x + 2 = 42 ⇒ 2x = 40

∴ x = 20 = an even number, which goes against our supposition.

3. A mathematics teacher tabulated the marks secured by 35 students of 8th class. The average of their marks was 72. If the marks secured by Reema was written as 36 instead of 86 then find the correct average marks up to two decimal places.
(a) 73.41
(b) 74.31
(c) 72.43
(d) 73.43
(e) Cannot be determined
Ans.d

Correct average = \(\frac{35 \times 72 + \left(86 - 36\right)}{35}\)

≈ 72 + 1.43 = 73.43

4. The average of five consecutive odd numbers is 61. What is the difference between the highest and the lowest number?
(a) 8
(b) 2
(c) 5
(d) Cannot be determined
(e) None of these
Ans.a

Suppose the consecutive odd numbers are : x, x + 2, x + 4, x + 6 and x + 8

Therefore, the required difference = x + 8 – x = 8

Note that answering the above question does not require the average of the five consecutive odd numbers.

5. In a coconut grove, (x + 2) trees yield 60 nuts per year, x trees yield 120 nuts per year and (x – 2) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x.
(a) 3
(b) 4
(c) 5
(d) 6
(e) None of the above
Ans.e

\(\frac{\left ( x + 2\right ) \times 60 + x \times 120 + \left ( x - 2 \right ) \times 180}{\left ( x + 2\right ) + x + \left ( x - 2\right )} = 100\)

\(\frac{360x - 240}{3x}\) = 100

⇒ 60x = 240 ⇒ x = 4

6. 30 pens and 75 pencils were purchased for 510. If the average price of a pencil was 2.00, find the average price of a pen.
(a) 10
(b) 11
(c) 12
(d) cannot be determined
(e) None of the above
Ans.c

Since average price of a pencil = 2

∴ Price of 75 pencils = 150

∴ Price of 30 pens = (510 – 150) = 360

∴ Average price of a pen = 36060 = 12

7. A school has 4 section of Chemistry in Class X having 40, 35, 45 and 42 students. The mean marks obtained in Chemistry test are 50, 60, 55 and 45 respectively for the 4 sections. Determine the overall average of marks per student.
(a) 50.25
(b) 52.25
(c) 51.25
(d) 53.25
(e) None of the above
Ans.b

Required average marks

= \(\frac{40 \times 50 + 35 \times 60 + 45 \times 55 + 42 \times 45}{40 + 35 + 45 + 42}\)

= \(\frac{2000 + 2100 + 2475 + 1890}{162}\)

= 8465162 = 52.25

8. The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
(a) 0
(b) 1
(c) 10
(d) 19
(e) None of the above
Ans.d

Average of 20 numbers = 0.

∴ Sum of 20 numbers = (0 × 20) = 0.

It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (–a).

9. The average of six numbers is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers?
(a) 4.5
(b) 4.6
(c) 4.7
(d) 4.8
(e) None of the above
Ans.b

Sum of the remaining two numbers

= (3.95 × 6) – [(3.4 × 2) + (3.85 × 2)]

= 23.70 – (6.8 + 7.7)

= 23.70 – 14.5 = 9.20

∴ Required average = (9.22) = 4.6

10. Nine persons went to a hotel for taking their meals. Eight of them spent 12 each on their meals and the ninth spend 8 more than the average expenditure of all the nine. What was the total money spent by them?
(a) 115
(b) 117
(c) 119
(d) 122
(e) None of the above
Ans.b

Let the average expenditure of all the nine be x.

Then, 12 × 8 + (x + 8) = 9x or 8x = 104 or x = 13.

∴ Total money spent = 9x = (9 × 13) = 117.