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31. A has 50 coins of 10 paise denominations. While B has 10 coins of 50 paise denominations. C has 20 coins of 25 paise denominations while D has 25 coins of 20 paise denominations. The average number of paise per person is :

A. 450 paise

B. 500 paise

C. 550 paise

D. 650 paise

Discuss

Solution:

\begin{aligned} \frac{[(10 \times 50) + (50 \times 10) + (20 \times 25) + (25 \times 20)]}{4} \\ = 500 paise \end{aligned}

32. The average income of A, B and C is Rs. 12,000 per month and average income of B, C and D is Rs. 15,000 per month. If the average salary of D be twice that of A, then the average salary of B and C is in Rs. :

A. 8,000

B. 18,000

C. 13,500

D. 9,000

Discuss

Solution:

\begin{aligned} A + B + C = 12000 \times 3 \\ B + C + D = 15000 \times 3 \\ \to D - A = 3000 \times 3 = 9000 \\ Also, D = 2 A \\ Then, D = 18000 and A = 9000 \\ Therefore, \\ Average salary of B and C, \\ = \frac{45000 - 18000}{2} \\ = 13500 \end{aligned}

33. A passenger travels from Delhi to Merut at a speed of 30 kmph and return with a speed of 60 kmph. What is the average speed?

A. 40

B. 45

C. 50

D. 48

Discuss

Solution:

Average Speed

\begin{aligned} = \frac{2 \times 60 \times 30}{60 + 30} \\ = \frac{3600}{90} \\ = 40 kmph \end{aligned}

34. The average of 20 students is 12 years, if the teacher's age is included, average increases by one. The age of the teacher is:

A. 30 years

B. 33 years

C. 28 years

D. 35 years

Discuss

Solution:

Average of 20 students = 12 years
Total age of 20 students
= 20 × 12
= 240 years
When teacher included average become 13 years
Now, total age 20 students and teacher
= 13 × 21= 273 years
∴ Age of teacher
= 273 - 240
= 33 years

35. The average wages of a worker during a fortnight comprising 15 consecutive working days was Rs. 90 per day. During the first 7 days, his average wages was Rs. 87/day and the average wages during the last 7 days was Rs. 92/day. What was his wage on the 8^th day?

A. 93

B. 90

C. 92

D. 97

Discuss

Solution:

The total wages earned during the 15 days that the worker worked ,
= 15 × 90 = Rs. 1350
The total wages earned during the first 7 days = 7 × 87 = Rs. 609
The total wages earned during the last 7 days = 7 × 92 = Rs. 644

Total wages earned during the 15 days,
= wages during first 7 days + wage on 8^th day + wages during the last 7 days.

1350 = 609 + wage on 8^th day + 644
wage on 8^th day = 1350 - 609 - 644 = Rs. 97

36. 40% of the employees in a factory are workers. All the remaining employees are executives. The annual income of each worker is Rs. 390. The annual income of each executive is Rs. 420. What is the average annual income of all the employees in the factory together?

A. 390

B. 405

C. 408

D. 415

Discuss

Solution:

Let X be the number of employees.
We are given that 40% of the employees are workers.
Now, 40% of X is

\frac{40}{100}

× X = 0.4X
Hence, the number of workers is

\frac{2 X}{5}

All the remaining employees are executives,
so the number of executives equals,
(The number of Employees)

-

(The number of Workers)
= X

-

\frac{2 X}{5}

\frac{3 X}{5}

The annual income of each worker is Rs. 390.
Hence, the total annual income of all workers together is
=

\frac{2 X}{5}

× 390 = 156X
Also, the annual income of each executive is Rs.420.
Hence, the total income {of all the executives together is,
=

\frac{3 X}{5}

× 420 = 252X
Hence, the total income of the employees is,
= 156X + 252X = 408X
The average income of all the employees together = 408

37. The average price of 10 books is Rs.12 while the average price of 8 of these books is Rs.11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what is the price of each of these two books?

A. Rs. 5, Rs.7.50

B. Rs. 8, Rs. 12

C. Rs. 16, Rs. 10

D. Rs. 12, Rs. 14

Discuss

Solution:

Total cost of 10 books = Rs. 120
Total cost of 8 books = Rs. 94
⇒ The cost of 2 books = Rs. 26
Let the price of each book be x and y.
⇒ x + y = 26 - - - - - - (1)

(\frac{160}{100}) x + y = 26

On Solving for y, we get
y = 10
Now, Substituting y = 10 in (1) we get,
x + 10 = 26
x = 16
So the price of each book is Rs. 16 and Rs. 10 respectively.

38. In a set of three numbers, the average of first two numbers is 2, the average of the last two numbers is 3, and the average of the first and the last numbers is 4. What is the average of three numbers?

A. 2

B. 2.5

C. 3

D. 3.5

Discuss

Solution:

\begin{aligned} Let the three numbers be x, y, and z . \\ We are given that \\ \frac{x + y}{2} = 2 \\ \frac{y + z}{2} = 3 \\ \frac{x + z}{2} = 4 \\ Adding three equations, \\ \frac{x + y}{2} + \frac{y + z}{2} + \frac{x + z}{2} = 2 + 3 + 4 \\ x + y + z = 9 \\ The average of the three numbers is, \\ \frac{x + y + z}{3} = \frac{9}{3} = 3 \end{aligned}

39. Of the three numbers, the first is twice the second and the second is twice the third. The average of the reciprocal of the numbers is $\frac{7}{72}$ . The numbers are:

A. 36, 18, 9

B. 24, 12, 6

C. 20, 10, 5

D. 16, 8, 4

Discuss

Solution:

\begin{aligned} Let three numbers be x, y, z . \\ Given, \\ x = 2 y \\ \Rightarrow x = 4 z \\ \Rightarrow y = 2 z \\ \Rightarrow z = z \\ The average of reciprocal numbers is \frac{7}{72} \\ \frac{\frac{1}{x} + \frac{1}{y} + \frac{1}{z}}{3} = \frac{7}{72} \\ \Rightarrow \frac{y z + x z + x y}{3 x y z} = \frac{7}{72} \\ \Rightarrow \frac{2 z \times z + 4 z \times z + 4 z \times 2 z}{3 (4 z \times 2 z \times z)} = \frac{7}{72} \\ \Rightarrow \frac{2 z^{2} + 4 z^{2} + 8 z^{2}}{3 \times 8 z^{3}} = \frac{7}{72} \\ \Rightarrow \frac{14 z^{2}}{24 z^{3}} = \frac{7}{72} \\ \Rightarrow 504 = 84 z \\ z = 6 \\ So, x = 4 z = 4 \times 6 = 24, \\ \Rightarrow y = 2 z = 2 \times 6 = 12 \\ Thus the numbers are 24, 12, 6 \end{aligned}

40. The average monthly salary of 12 workers and 3 managers in a factory was Rs. 600. When one of the manager whose salary was Rs. 720, was replaced with a new manager, then the average salary of the team went down to 580. What is the salary of the new manager?

A. 640

B. 690

C. 420

D. 570

Discuss

Solution:

The total salary amount = 15 × 600 = 9000
The salary of the exiting manager = 720
Therefore, the salary of 12 workers and the remaining 2 managers,
= 9000 − 720 = 8280
When a new manager joins, the new average salary drops to Rs. 580 for the total team of 15 of them
The total salary for the 15 people i.e., 12 workers, 2 old managers and 1 new manager =580 × 15 = 8700
Therefore, the salary of the new manager is,
9000 - 8700 = 300 less than that of the old manager who left the company, which is equal to 720 - 300 = 420

Alternatively,
The average salary dropped by Rs. 20 for 15 of them.
Therefore, the overall salary has dropped by 15 × 20=300
Therefore, the new manager's salary should be Rs. 300 less than that of the old manager,
= 720 - 300
= 420

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