Average test 5-Solved questions with detailed explanations for SSC, IBPS, SBI PO, RRB, RBI, CSE, CGL, CHSL, CDA, CSE, UPSC

16)

The average of 30 numbers is 40 and that of either 40 numbers is 30. The average of all the numbers is ?

A)
35
B)
34.5
C)
34
D)
34 $\frac{2}{7}$
E)
None of these

Answer: Option D

Explanation

According to the question,

$n_{1} = 30, A_{1} = 40, n_{2} = 40, A_{2} = 30$

We know the formula

Weighted average(Aw)= $\frac{n_{1} A_{1} + n_{2} A_{2}}{n_{1} + n_{2}}$

Average of all the 70 numbers

$= \frac{30 \times 40 + 40 \times 30}{30 + 40} = \frac{2400}{70} = 34 \frac{2}{7}$

Hence, Option D is correct.

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Discussion

17)

Average of 40 observations is 50 and average of another 60 observations is 55. The average of all observations is ?

A)
53
B)
50
C)
83
D)
62
E)
None of these

Answer: Option A

Explanation

Sum ofo 40 observations = 40×50=2000

and sum of 60 observations =60×55=3300

∴ Sum of 100 observations =2000+3300

=5300

Required average = $\frac{5300}{100}$ =53

Hence, Option A is correct.

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Discussion

18)

The average marks obtained by 8 students in a certain examination is 51. The average marks obtained by another 9 students is 68. What will be the average marks obtained by all the students?

A)
60
B)
60.5
C)
59
D)
59.5
E)
None of these

Answer: Option A

Explanation

Given,

$n_{1} = 8, a_{1} = 51, n_{2} = 9, a_{2} = 68$

According to the formula

Required average = $\frac{n_{1} a_{1} + n_{2} a_{2}}{n_{1} + n_{2}}$

$= \frac{8 \times 51 + 9 \times 68}{8 + 9} = \frac{408 + 612}{17} = \frac{1020}{17}$

=60

Hence, Option A is correct.

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Discussion

19)

Akash bought 5 pants at ₹ 25 each, 10 shirts at ₹ 50 each and 15 ties at ₹ 35 each. Find the average price of all the articles?

A)
₹ 60
B)
₹ 45
C)
₹ 38.33
D)
₹ 45.33
E)
None of these

Answer: Option C

Explanation

Given,

$n_{1} = 5, n_{2} = 10, n_{3} = 15, a_{1} = 25, a_{2} = 50, a_{3} = 35$

According to the formula,

Average price= $\frac{n_{1} a_{1} + n_{2} a_{2} + n_{3} a_{3}}{n_{1} + n_{2} + n_{3}}$

$= \frac{5 \times 25 + 10 \times 50 + 15 \times 35}{5 + 10 + 15} = \frac{25 + 100 + 105}{1 + 2 + 3} = \frac{230}{6}$

= 38.33

Hence, Option C is correct.

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Discussion

20)

A class is divided into two sections A and B. Passing average of 20 students of section A is 80% and passing average of 30 students of section B is 70%. What is the passing average of both the sections?

A)
74%
B)
72%
C)
75%
D)
77%
E)
None of these

Answer: Option A

Explanation

Given,

$n_{1} = 20, n_{2} = 30, a_{1} = 80 %, a_{2} = 70 %$

We know the formula

Weighted average(Aw)= $= \frac{n_{1} a_{1} + n_{2} a_{2}}{n_{1} + n_{2}}$

∴ Total average

$= \frac{20 \times 80 + 30 \times 70}{20 + 30} = \frac{1600 + 1200}{50} = 74 %$

Hence, Option A is correct.

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Discussion

Average Test-5 (Calculating weighted average)

Answer: Option D

Answer: Option A

Answer: Option A

Answer: Option C

Answer: Option A