Test: Averages - 2 - UCAT MCQ

Let the runs scored by Sumit in the third match be x.

According to the question,

Average runs scored by Sumit in 5 matches = (Total suns scored by Sumit in 5 matches)/5

So, Total runs scored by Sumit in 5 matches = 5 × (Average runs scored by Sumit in 5 matches)

⇒ 5 × 90

⇒ 450 runs

again, According to the question

Total runs scored by Sumit in 5 matches = Runs scored in first 2 matches + x + Runs scored in last 2 matches

⇒ 450 = 200 + x + 150

⇒ x = 450 – 350

⇒ x = 100 runs

∴ The runs scored by Sumit in the third match is 100 runs. 

Let the average age of 6 persons be q

Now, according to the question

⇒ 24 × 45 + 6 × (q) = 30 × (45 × 120/100)

⇒ 1080 + 6 × (q) = 30 × 54

⇒ 1080 + 6 × (q) = 1620

⇒ 6 × (q) = 1620 – 1080

⇒ 6 × (q) = 540

⇒ q = 90

∴ The average of 6 persons is 90 

Let the average of 8 people be x kg.

And, the weight of the new person is y kg.

Sum of 8 person weight = [8 × (x)] = 8x kg.

When the person is replaced 

⇒ 8x + y - 65 = 8 × (x + 2.5)

⇒ 8x + y - 65 = 8x + 20

⇒ y = 85 kg.

∴ The weight of the new person is 85 kg.

The total weight of P and his three friends = 55 × 4 = 220 kg

Let, the average weight of three friends = x

So, the total weight of three friends = 3x

The weight of P = x + 4

Then, (x + 4) + 3x = 220

⇒ 4x + 4 = 220

⇒ 4x = 220 - 4 = 216

⇒ x = 216/4 = 54

∴ P's weight = 4 + 54 = 58 kg

∴ The P's weight (in kg) is 58 kg

The total sum of all 45 number = 150 × 45 = 6750

Now, 46 is wrongly written as 91

The correct sum of data = 6750 – (91 – 46) = 6705

Then, Correct average of the data = 6705/45 = 149

∴ The correct average is 149

The sum of nine numbers = 60 × 9 = 540

The sum of the first five numbers = 55 × 5 = 275

The sum of the next three numbers = 65 × 3 = 195

Ninth number = (540 – 275 – 195) = (540 – 470) = 70

∴ Tenth number = 70 + 10 = 80

Value of 14th number = (Sum of first 14 numbers +  Sum of last 15 numbers) - Sum of 28 numbers  

⇒ 14th Number = (14 × 74 + 15 × 84 - 28 × 77)

⇒ 1036 + 1260 - 2156 = 140 

Average of remaining 27 numbers = (Sum of 28 numbers - 14th number) ÷ 27 

⇒ (2156 - 140) ÷ 27 = 2016 ÷ 27 

⇒ 74.66 or 74.7

The average weight of 8 students increased by 1.5 kg.

Sum = 8 × 1.5 = 12

New average = 12 + 65

Weight of new student = 77 kg.

Let the total number of students in the class be x.

⇒ Average weight of all students = 68.5 kg

Total weight of all students = 68.5x kg

Total weight of four students = (72.2 + 70.8 + 70.3 + 66.7) kg = 280 kg

According to the question,

⇒ 68.5x + 280 = 68.8 (x + 4)

⇒ 68.5x + 280 = 68.8x + 275.2

⇒ x = 16

∴ Total number of students initially is 16.

Let age of P, Q, R and S be P, Q, R and S respectively.

Given,

⇒ P + Q + R = 24 × 3

⇒ P + Q + R = 72

Then,

⇒ P + Q + R + S = 30 × 4 = 120

⇒ S = 120 - 72 = 48 Years

The age of S is 48 years.

⇒ T = 48 + 4 = 52 years

Total age of five persons =

= 120 + 52

= 172

Average age of 5 persons = 172/5 = 34.4 years