BANK & INSURANCE (AVERAGE) PART 3

⇒ Average = sum of elements / number of elements

Given
There are 2500 raincoats, 1500 schoolbags and 1000 water bottles were ordered in a month.
Out of this, 60% of raincoats, 75% of schoolbags and 80% of water bottles were sold out.

Number of sold raincoats = (60/100) × 2500
= 1500

Number of sold schoolbags = (75/100) × 1500
= 1125

Number of sold water bottles = (80/100) × 1000
= 800

The price of a raincoat, a school bag and a water bottle is Rs. 300, Rs. 400 and Rs. 120.

Total price of 300 raincoats
= 300 × 1500 = Rs. 450000

Total price of 400 schoolbags
= 400 × 1125 = Rs. 450000

Total price of 120 water bottles = 120 × 800
= Rs. 96000

Total price including all three sold items
= 450000 + 450000 + 96000 = 996000

Total number of items = 1500 + 1125 + 800
= 3425

Average income of that shop for that particular month. = (996000/3425) = 290.8

Average income of that shop for that particular month is Rs. 290.8

Let the daily earning of museum for that particular week is d1, d2, d3, d4, d5, d6 and d7 respectively.

Given, Average earning for the first two days of week is Rs. 750 :

Average = total earning / number of days
⇒ Total earning of first two days of week = d1 + d2 = Rs. 1500

Given, The average earning for last two days is Rs. 1800:
⇒ Total earning of last two days of week
= 1800 × 2 = Rs. 3600

⇒ Total earning of first two days of week
= d6 + d7 = Rs. 3600

Given, Sum of total earning of third, fourth and fifth day is 1/3rd of total earning of last two days:

⇒ (d3 + d4 + d5) = 1/3 × (d6 + d7)
⇒ (d3 + d4 + d5) = 1/3 × (3600)
⇒ (d3 + d4 + d5) = 1200

Total earning for all seven days of week:
⇒ d1 + d2 + d3 + d4 + d5 + d6 + d7
⇒ 1500 + 1200 + 3600
⇒ Rs. 6300

∴ Total earning for all seven days of week is Rs. 6300.

Average earning for a week = total earning for seven days/7
⇒ 6300/7 = 900

∴ Average earning for a week is Rs. 900.

Let the number of items sold by Ram in a day be x and total amount earned after selling all items except one wrongly calculated price item be Rs. m.

Average price of all items sold in a day = old average = (total amount earned after selling all items)/number of items = (m + 150)/x

Given, The cost of one sold item is wrongly calculated as 150 instead of 250,
so average price is decreased by Rs. 10

Average of all items with new price 250
= new average

= (total amount earned after selling all items)/(x)

= {(m + 250)/x}

Old average + 10 = new average

⇒ (m + 150)/x + 10 = (m + 250)/x

⇒ (m + 150) + 10x = (m + 250)

⇒ 150 + 10x = 250

⇒ 10x = 100

⇒ x = 10

∴ Number of all sold items by Ram in a day is 10.

Let the numbers be p, q, r, s and t According to question

⇒ (p + q + r)/3 = {(r + s + t)/3} − 20

⇒ p + q + r = r + s + t − 60

⇒ p + q = s + t − 60 ........ 1

Given
⇒ r + s + t = 65

⇒ s + t = 65 − r ........ 2

Putting the value of s + t in 1 we get

⇒ p + q = 65 − r − 60

⇒ p + q + r = 5

Let the average weight of all the students = x kg.

Total weight of students = 20x kg

Average weight of students including class teacher = (x + 2) kg

Total weight of students including class teacher
= (x + 2) × 21 kg = (21x + 42) kg

After replacement, average weight of students including class teacher = (x + 1.5) kg

After replacement, total weight of students including class teacher
= (x + 1.5) × 21 kg = 21x + 31.5 kg

Difference of total weights = (21x + 42) − (21x + 31.5) kg = 10.5 kg