Q1. The average age of a family of 6 members is 22 years. If the age of the youngest member be 7 years, then what was the average age of the family at the birth of the youngest member?
Answer: B
Explanation:
Total age of all members = [latex] 6 \times 22 [/latex]= 132 years
7 years ago, total sum of ages = 132 – [latex](6 \times 7) [/latex] = 90 years
But at that time there were 5 members in the family
Average at that time = [latex] \frac {90} {5} [/latex] = 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 [latex] \Rightarrow [/latex] 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?
A. 450
B. 420
C. 430
D. 410
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= [latex] \frac {(35a + 42)}{(35 + 7)} [/latex]
Now, we have [latex] \frac {(35a + 42)}{42} [/latex] = (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:
A. 51.4
B. 52.6
C. 56.1
D. 55.3
Answer: A
Explanation:
Let the required mean score be a
Then, [latex] 20 \times 80 + 25 \times 31 + 55 \times a = 52 \times 100 [/latex]
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:
A. 0 , 7
B. 0 , 6
C. 5 , 7
D. 0 , 9
Answer: D
Explanation:
Let the number be x.
Then, [latex] \frac {(x + {x}^{2})}{2} = 5x [/latex]
[latex] {x}^{2} – 9x [/latex] = 0
[latex] x (x – 9) [/latex] = 0
[latex] x = 0 or x [/latex] = 9.