BANK & INSURANCE (AVERAGE) PART 2

Total Questions: 45

1. The average weight of some girls in a group is 25.5 kg. If 4 girls with an average of 23.2 kg leave the group and 5 girls with an average weight of 31.66 kg join the group the average of the group increases by 2 kg. What is the number of girls in the group initially?

Correct Answer: (b) 19  
Solution:

let x be the number of girls,
According to the question,
(25.5x-4 × 23.2+5 × 31.66)/(x+1)=25.5 + 2

(25.5x-92.8+158.3)/(x+1)=27.5

25.5x + 65.5 = 27.5 (x + 1)

25.5x + 65.5 = 27.5x + 27.5

27.5x - 25.5x = 65.5 - 27.5

2x = 38

x = 38/2

x = 19

Number of girls in the group is 19.
∴ The correct answer is 19.

2. There is a group of dogs playing in a pet house. Their average weight is 9.5 kg. If 5 dogs with an average weight of 6.5 kg leave the group by getting exhausted and 4 dogs of average weight 12.5 kg join the group, the average of the group increases by 3 kg. How many dogs were there in the group initially?

Correct Answer: (d) 10  
Solution:

Let the no. of dogs be x
According to the question,
(9.5x - 5 × 6.5 + 4 × 12.5) / (x - 5 + 4) = 12.5

⇒ (9.5x - 32.5 + 50) / (x - 1) = 12.5

⇒ 9.5x + 17.5 / (x - 1) = 12.5

⇒ 9.5x + 17.5 = (x - 1) × 12.5

⇒ 12.5x - 9.5x = 17.5 + 12.5

⇒ 3x = 30 ⇒ x = 10

∴ The number of dogs initially in the group is 10.

3. The average age of employees is 28 years. The average age of male employees is 15 years and that of the female employees is 32 years. Find the ratio of the male employees to female employees.

Correct Answer: (a) 4 : 13  
Solution:

Let the number of male employees is x and female employees is y.
Sum of the ages of male = 15x
Sum of the ages of female = 32y

According to question:
⇒ 28(x + y) = 15x + 32y

⇒ 28x + 28y = 15x + 32y

⇒ 13x = 4y

⇒ x/y = 4/13

⇒ x : y = 4 : 13

∴ Ratio of male employees to female employees is 4:13.

4. The average salary of 10 employees was found to be Rs 20,000. Later on, it was found that the salary of two employees was recorded as Rs 2,000 and Rs 2,500 instead of Rs 20,000 and Rs 5,200. Find the correct average salary.

Correct Answer: (c) Rs 22070
Solution:

Total salary of 10 employees = Rs 20,000 × 10
= Rs 2,00,000

Value of wrong items = Rs (2,000 + 2,500)
= Rs 4,500

Value of correct items = Rs (20,000 + 5,200)
= Rs 25,200

∴ Correct average salary = Rs (2,00,000 - Rs 4,500 + Rs 25,200)/10 = Rs 22,070

5. Average age of P, Q and R is 90 years. When S joins them the average age becomes 86 years. A new person T whose age is 6 years more than S, replaces P and the average of P, Q, R, S and T becomes 84 years. What is the age of P?

Correct Answer: (a) 88 years  
Solution:

Average age of P, Q and R = 90 years
⇒ (P + Q + R)/3 = 90
⇒ P + Q + R = 270

Similarly, Average age of P, Q, R and S = 86 years
⇒ (P + Q + R + S)/4 = 86
⇒ P + Q + R + S = 344

⇒ Age of P, Q, and R + Age of S = 344

⇒ 270 + S = 344

⇒ S = 74 years

If the age of S is 74 year
Then the Age of T = 74 + 6 = 80 years

Similarly, Average age of Q, R, S and T = 84 years
⇒ (Q + R + S + T)/4 = 84

⇒ Q + R + S + T = 336

⇒ Q + R + 74 + 80 = 336 (Putting the value of S, and T)

⇒ Q + R = 182

⇒ Age of P, Q, and R = 270

⇒ P + Q + R = 270 (Putting the value of Q + R from above)

⇒ P + 182 = 270

⇒ P = 88 years

∴ Age of P is 88 Years.

6. The average score of top 6 batsmen of Indian cricket team in a match is 46. If the 7th batsman is included, the average becomes 50. If the 8th batsman comes and scores 34 runs, then find the ratio of the average scores of top 6 and top 8 batsmen.

Correct Answer: (c) 23:24
Solution:

According to question,
Sum of scores of top 6 / 6 = 46
⇒ Sum of scores of top 6 = 276

Now, average after 7th batsman included = 50
∴ Sum of scores of top 7 / 7 = 50
∴ Sum of scores of top 7 = 350

Now, total score of top 8 batsmen
= 350 + 34 = 384

∴ Average score of top 8 batsmen
= sum of scores / 8
= 384/8

⇒ 48

∴ Required ratio = 46:48 = 23:24

∴ The ratio of averages of top 6 and top 8 batsmen is 23:24

7. The average age of all workers in a company is 46 years. The average age of all 75 men workers is 50 years and the average age of all women workers is 40 years. If 24 women are married, then how many women workers are unmarried?

Correct Answer: (a) 26  
Solution:

Sum of the total ages of all the male workers = 75 × 50 = 3750 years

Let the number of unmarried women workers = x

Therefore, the sum of the total ages of all the women workers = (x + 24) × 40 = (40x + 960) years

ATO, 3750 + (40x + 960) = 46 × (x + 24 + 75):
⇒ 40x + 4710 = 46x + 4554
⇒ 6x = 156
⇒ x = 26
Hence, the correct answer is 26.

8. There are three numbers where the first number is twice of the second number and thrice of the third number. If their average is 88, then find the ratio of second number and the difference of first and third number.

Correct Answer: (d) 3:4  
Solution:

Let the 1st number = x
Then, 2nd number = x/2
And 3rd number = x/3
∴ Average = (x + x/2 + x/3)/3 = 88
⇒ 6x + 3x + 2x /18 = 88
⇒ 11x / 18 = 88
⇒ x = 88 × 18/11
⇒ x = 144
∴ 1st number = 144
2nd number = 144/2 = 72
3rd number = 144/3
∴ Difference between 1st & 3rd number = 144 - 144/3
⇒ 288/3
⇒ 96
∴ Required ratio = 72/96
⇒ 3/4 or 3:4
∴ The ratio of 2nd number and difference of 1st and 3rd number is 3:4

9. Average of 75 numbers are 44. When 5 more numbers are included, the average of 80 numbers become 46. Find the average of 5 numbers.

Correct Answer: (d) 76  
Solution:

Let, average of 5 numbers = x
According to the question,
⇒ 75 × 44 + 5 × x = 80 × 46
⇒ 3300 + 5x = 3680
⇒ 5x = 380
⇒ x = 76
∴ Average of 5 numbers = 76

10. Narender marks were wrongly entered as 83 and 78 instead of 63 and 58. If the average marks calculated for the whole class increased by two, then what is the number of students in the class?

Correct Answer: (b) 20  
Solution:Let, the number of students in the class be x
As the average increases by 2
Wrong value is 83 and 78
True value is 63 and 58
The total increase in marks for x students
⇒ x × average increases by 2
⇒ x × 2 = 2x
Total increase marks by adding true value at the place
of wrong value
⇒ 2x = (83 + 78) - (63 + 58)
⇒ 2x = 161 - 121
⇒ x = 20
∴ We assumed that the number of students in the class be x
∴ The number of students in the class is 20.