BANK & INSURANCE (AVERAGE) PART 2

Total Questions: 45

41. Akash on his birthday distributed on an average 10 toffees per student. If on the arrival of the teacher and the headmaster to whom Akash gave 15 and 20 toffees respectively, the average toffee distributed per head increases to 11.5, then what is the number of students among whom the sweets were distributed?

Correct Answer: (a) 8  
Solution:Let’s assume that initial number of students be x.
∴ number of toffees given to x students = 10x
After the arrival of teacher and headmaster, total toffees distributed
= 10x + 15 + 20 = 10x + 35
Now, the average becomes 11.5,
∴ 10x + 35 = 11.5 × (x + 2)
⇒ 10x + 35 = 11.5x + 23
⇒ x = 8
∴ the number of students among whom the sweets were distributed is 8.

42. The average weight of 3 men A, B and C is 96kg. Another man D joins the group and the average now becomes 88 kg. If another man E, whose weight is 4 kg more than that of D, replace A, then the average weight of B, C, D and E becomes 82 kg. The weight of A is:

Correct Answer: (c) 92 kg
Solution:Let the weights of A, B, C, D, E be a, b, c, d, e kgs respectively.
We know that, Average = (Sum of all terms) / (Number of terms)
∴ Sum of all terms = Average × number of terms
∴ Average of a, b, c is 96, a + b + c = 3 × 96 = 288
∴ Average of a, b, c, d is 88, a + b + c + d = 4 × 88 = 352
∴ d = 352 - 288 = 64
∴ e is 4 more than d, e = 64 + 4 = 68
Now, since the average of b, c, d, e is 82, b + c + d + e = 4 × 82 = 328
∴ b + c = 328 - d - e = 328 - 64 - 68
⇒ b + c = 196
a = (a + b + c) - (b + c) = 288 - 196 = 92
Weight of A = 92 Kg

43. A man’s average expenditure for the first 5 months of the year was Rs. 175. For the next 3 months the average monthly expenditure was Rs. 27.33 more than what it was during the first 5 months. If the person spent Rs. 693 in all during the remaining 4 months of the year, find what percentage of his annual income of Rs. 2500 saved in the year.

Correct Answer: (d) 13%  
Solution:Average expenditure in first 5 months = Rs. 175
Total expenditure in first 5 months
= Rs. 175 × 5 = Rs. 875
Average expenditure in next 3 months
= Rs. 175 + Rs. 27.33 = Rs. 202.33
Total expenditure in next 3 months = Rs. 202.33 × 3
= Rs. 607
Total Expenditure in last 4 months = Rs. 693
Annual Expenditure = 875 + 607 + 693 = Rs. 2175
Annual Income = 2500 % savings
= (Annual Income - Annual Expenditure) × 100/Annual Income
= (2500 - 2175) × (100/2500) = 325/25 = 13%

44. Average salary of an employee in a company is Rs. 30,000. All the employees are divides into three tiers each have different increments. If the average increment is 6% and the difference in increment in each tier is 1%. What is the average salary after increment if there is equal number of employees in each tier and total employees are 90?

Correct Answer: (c) 31,800
Solution:Total salary of all the employees is Rs. 30,000 × 90 = 27,00,000
Total increment in first section = 30,000 × 30 × 0.05 = 45,000
Total increment in second section = 30,000 × 30 × 0.06 = 54,000
Total increment in third section = 30,000 × 30 × 0.07 = 63,000
Total increment = 1,62,000
Total salary after increment = 27,00,000 + 1,62,000 = 28,62,000
∴ Average salary = 28,62,000/90 = 31,800

45. There are five cricket bats available in a shop. The average price of these 5 bats is Rs. 800. The difference between price of the costliest and cheapest bat is Rs. 1700 and the price of the rest 3 bats are equal. The price of the cheapest bat is a perfect square number and its value is lying between Rs. 350 and Rs 500. Also the price of all the bats is in whole numbers (that is in integer value). Find the price of the costliest bat.

Correct Answer: (c) Rs. 2100
Solution:

Let the price of the costliest bat = x
Let the price of the cheapest bat = y
Let the price of each of the 3 remaining bat = z
Average price of all 5 bats = 800 (given)
Total cost of all the five bats = Average × 5
⇒ 800 × 5 = 4000
⇒ x + y + z + z + z = 4000
⇒ x + y + 3z = 4000 ---- (I)

It is also given the price of the cheapest bat is a perfect square number and greater than 350 and less than 500
Possible values of y = 361, 400, 441, 484

The difference between the price of the costliest bat and the cheapest bat is
= 1700 (given)
⇒ x - y = 1700

Taking value of y = 361
⇒ x = y + 1700 ⇒ x = 361 + 1700
⇒ x = 2061

Putting values of x and y in (I)
⇒ 2061 + 361 + 3z = 4000
⇒ 3z = 4000 - 2462
⇒ 3z = 1538
⇒ z = 1538/3
⇒ z = 512.667

But the price of all the bats must be in whole numbers (given):
⇒ Value of y can’t be = 361

Taking value of y = 400
⇒ x = y + 1700

⇒ x = 400 + 1700
⇒ x = 2100

Putting values of x and y in (I)
⇒ 2100 + 400 + 3z = 4000
⇒ 3z = 4000 - 2100 - 400
⇒ 3z = 1500
⇒ z = 500

The value of z comes out to be = 500, which is a whole number
The price of each of the remaining 3 bats = Rs 500
The price of the costliest bat = Rs. 2100
The price of the cheapest bat = Rs. 400
No other value satisfies the option
∴ The price of the costliest bat = x = Rs. 2100