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

21)

In an examination, a batch of 60 students made an average score of 55 and another batch of 40 made it only 45. What is the overall average score?

A)
52
B)
40
C)
56
D)
51
E)
None of these

Answer: Option D

Explanation

According to the question

$n_{1} = 60, n_{2} = 40, a_{1} = 55, a_{2} = 45$

We know the formula,

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

Average of combined group = $\frac{60 \times 55 + 40 \times 45}{60 + 40} = 51$

Hence, Option D is correct.

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Discussion

22)

There are 30 boys and 60 girls in a class. If the average age of boys is 12 yr and average age of girls is 10 yr, Find out the average age of the whole class?

A)
55.32 yr
B)
10.66 yr
C)
84 yr
D)
45 yr
E)
None of these

Answer: Option B

Explanation

According to the question

$n_{1} = 30, n_{2} = 60, a_{1} = 12, a_{2} = 10$

We know the formula,

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

Average age of the whole class

$= \frac{30 \times 12 + 60 \times 10}{30 + 60} = \frac{360 + 600}{90} = \frac{960}{90}$

= 10.66 yr

Hence, Option B is correct.

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Discussion

23)

Jenny bought 20 books at the rate of ₹ 10 each, 45 pens at the rate of ₹ 5 each and 15 pencils at the rate of ₹ 3 each. Calculate the average price of all the stationary goods?

A)
₹ 5.875
B)
₹ 55.60
C)
₹ 96
D)
₹ 78.65
E)
None of these

Answer: Option A

Explanation

According to the question

$n_{1} = 20, n_{2} = 45, n_{3} = 15, a_{1} = 10, a_{2} = 5, a_{3} = 3$

We know the formula,

Weighted average(Aw) $= \frac{n_{1} a_{1} + n_{2} a_{2} + n_{3} a_{3}}{n_{1} + n_{2} + n_{3}}$

Average price of all the stationary goods

$= \frac{20 \times 10 + 45 \times 5 + 15 \times 3}{20 + 45 + 15} = \frac{200 + 225 + 45}{80} = \frac{470}{80}$

= 5.875 yr

Hence, Option A is correct.

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Discussion

24)

A man bought 13 shirts of ₹ 50 each, 15 pants of ₹ 60 each and 12 pairs of shoes at ₹ 65 a pair. Find the average value of each article?

A)
₹ 25.06
B)
₹ 101
C)
₹ 86.23
D)
₹ 58.25
E)
None of these

Answer: Option D

Explanation

According to the question

$n_{1} = 13, n_{2} = 15, n_{3} = 12, a_{1} = 50, a_{2} = 60, a_{3} = 65$

We know the formula,

Weighted average(Aw) $= \frac{n_{1} a_{1} + n_{2} a_{2} + n_{3} a_{3}}{n_{1} + n_{2} + n_{3}}$

Average $= \frac{13 \times 50 + 15 \times 60 + 12 \times 65}{13 + 15 + 12}$

= ₹ 58.25

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Discussion

25)

The average score of a cricketer in two matches is 27 and in three other matches is 32. Then find the average score in all the five matches?

A)
45
B)
65
C)
30
D)
90
E)
None of these

Answer: Option B

Explanation

According to the question

$n_{1} = 2, n_{2} = 3, a_{1} = 27, a_{2} = 32$

We know the formula,

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

Average in 5 matches $= \frac{2 \times 27 + 3 \times 32}{2 + 3} = \frac{54 + 96}{5}$ =30

Hence, Option B is correct.

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Discussion

Average Test-5 (Calculating weighted average)

Answer: Option D

Answer: Option B

Answer: Option A

Answer: Option D

Answer: Option B