Answer: B
Explanation:
Total age of all members = \( 6 \times 22 \)= 132 years
7 years ago, total sum of ages = 132 – \((6 \times 7) \) = 90 years
But at that time there were 5 members in the family
Average at that time = \( \frac {90} {5} \) = 18 years
Q2. A batsman in his 17th innings makes a score of 85 and thereby increases his average by 3. What is his average after 17 innings?
Answer: B
Explanation:
Let the average after 16th innings be a
then total score after 17th innings \( \Rightarrow \) 16a + 85 = 17 (a + 3)
a = 85 – 51 = 34
Average after 17 innings = a + 3 = 34 + 3 = 37
Q3. There were 35 students in a hostel. If the number of students increases by 7, the expenses of the mess increase by Rs 42 per day while the average expenditure per head diminishes by Rs 1. Find the original expenditure of the mess?
Answer: B
Explanation:
Suppose the average expenditure was Rs a.
Then total expenditure = 35 a
When 7 more students join the mess, total expenditure = 35a + 42
Now, the average expenditure= \( \frac {(35a + 42)}{(35 + 7)} \)
Now, we have \( \frac {(35a + 42)}{42} \) = (a – 1)
or, 35a + 42 = 42a – 42
7a = 84
a = 12
Q4. The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of the remaining 55% is:
Answer: A
Explanation:
Let the required mean score be a
Then, \( 20 \times 80 + 25 \times 31 + 55 \times a = 52 \times 100 \)
1600 + 775 + 55a = 5200
55a = 2825
a = 51.4
Q5. The average of a non-zero number and its square is 5 times the number. The number is:
Answer: D
Explanation:
Let the number be x.
Then, \( \frac {(x + {x}^{2})}{2} = 5x \)
\( {x}^{2} – 9x \) = 0
\( x (x – 9) \) = 0
\( x = 0 or x \) = 9.
Answer: A
Explanation:
We have :
\( \frac {(a + b + c)}{3} \) = M or (a + b + c) = 3 M.
Now, \( {(a + b + c)}^{2} \) = \( {(3 M)}^{2} = {9 M}^{2} \)
\( {a}^{2} + {b}^{2} + {c}^{2} + 2 (ab + bc + ca) = {9 M}^{2} \)
\( {a}^{2} + {b}^{2} + {c}^{2} = {9 M}^{2} \)
Required mean = \( \frac {({a}^{2} + {b}^{2} + {c}^{2})} {3} \) = \( \frac {{9 M}^{2}} {3} = {3 M}^ {2} \)
Q2. The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one them weighing 65 kg. What might be the weight of the new person?
Answer: C
Explanation:
Total weight increased = \( (8 \times 2.5) kg = 20 kg \)
Weight of new person = \( (65 + 20) kg = 85 kg \)
Q3. The average age of the boys in a class is 16 years and that of the girls is 15 years. The average age for the whole class is:
Answer: D
Explanation:
Clearly, to find the average, we ought to know the number of boys, girls or students in the class, neither of which has been given
So, the data provided is inadequate
Q4. A cricketer has completed 10 innings and his average is 21.5 runs. How many runs must he make in his next innings so as to raise his average to 24?
Answer: C
Explanation:
Total of 10 innings = \( 21.5 \times 10 \) = 215
Suppose he needs a score of a in \( {11}^{th} \) innings; then average in 11 innings = \( \frac {(215 + a)}{11} \)= 24
or, a = 264 – 215 = 49
Q5. Find the average of 13 + 26 + 39 + …….. + 260
Answer: A
Explanation:
\( \frac {13 (1 + 2 + 3 + ….. + 20)}{20 \times 2}\)
\(\frac {13 \times 20 \times 21}{40}\)
\(\frac {5460}{40} \) = 136. 5
Answer: B
Explanation:
Sum of the remaining two numbers = \( (3.95 \times 6) – [(3.4 \times 2) + (3.85 \times 2)] \)
= 23.70 – (6.8 + 7.7)
= 23.70 – 14.5 = 9.20
Average = \( \frac {9.2}{2} \) = 4.6
Q2. The average salary of the entire staff in an office is Rs 120 per month. The average salary of officers is Rs 460 and that of non-officer is Rs 110. If the number of officers is 15, then find the number of non-officer in the office?
Answer: C
Explanation:
Let the required number of non-officers = a
Then, \( 110a + 460 \times 15 \) = 120 (15 + a)
or, 120a – 110a = \( 450 \times 15 – 120 \times 15 \) = 15 (460 – 120)
or, 10a = \( 15 \times 340 \)
a = \( 15 \times 34 \) = 510
Q3. Find the average of first 20 multiple of 7?
Answer: B
Explanation:
Average = \( \frac { 7 (1 + 2 + 3 + ……. + 20)}{20} = 7 \times 20 \times \frac {21} {20 \times 2} = 73.5 \)
Q4. The average of four consecutive ODD number is 28.Find the largest number.
Answer: B
Explanation:
\(\frac {x + (x + 2) + (x + 4) + (x + 6)}{4}\) = 28
4x +12 = \( 28 \times 4 = > 112 \)
\(x = \frac {(112 – 12)}{4} = \frac {100}{4}\) 24
Largest number \(x + 6 = 25 + 6 = 31\)
Q5. Find the average of first 60 natural numbers
Answer: A
Explanation:
Sum of First 60 Natural numbers = \( \frac { n (n + 1)}{2}\)
\( \frac {60 \times 61}{2}\) = 1830
Average = \( \frac {1830}{60}\) = 30. 5
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