Robert Bosch Averages Quiz-3

Explanation:
Since the month begins with a saturday , So there will be 5 sundays in the month.
Required Average = \frac{430\times5+270\times26}{31}
= \frac{2150+7020}{31}
= \frac{2150+7020}{31}
= 295.80
Rounding off for Approx. Answer = 296 days
Therefore, Number of car enthusiasts per day is 296

Explanation:
Let the number of Jimmy’s family members be X.
Therefore, the total weight = X.Y
Equation in the 1st situation:
(X + 1) (Y + 1) = XY + 30
XY + X + Y + 1 = XY + 30
X + Y = 29 .....(i)
Equation in the 2nd situation:
(X + 1) (Y - 1) = XY + 18
XY + Y - X - 1 = XY + 18
Y - X = 19 ....(ii)
Solving equations (i) and (ii), we get
2Y = 48, Therefore, Y = 24.

Explanation:
Total age of 13 gamers= 36 × 13 = 468

Given that if the age of one more gamers is added the average decreases by half a year
∴ Total age of 14 gamers = 35.5 × 14 = 497

Now, Age of the new gamers = 497 – 468 = 29 years

Explanation:
If the average of ‘N’ number is equal to ‘X’ when a quantity is removed the average becomes ‘Y’. Then the value of the removed number is [N (X – Y) + Y].

Given:
Number of persons = N = 15
Old average = X = 15
New average = Y = 14
Difference in average = (X – Y) = 1

By the Shortcut approach, we get
[n (X – Y) + Y]
[15 × (1) + 14] years = 29 years.

Explanation:
Let Tyrion weighs X kg.
According to Tyrion , 55 < X < 62
According to Tyrion's father, 50 < X < 60
According to Tyrion's sister, X < 58
The values satisfying all the above conditions are 56 & 57.
Resultant Average = (\frac{56+57}{2}) = \frac{113}{2}
So, the required average weight of Tyrion Lannister is 56.5 kg.

Explanation:
Let the age of Ryan, Karren and Chris = A,B and C
A + B = 2 × 20 = 40 yr
B + C = 2 × 19 = 38 yr
C + A = 2 × 21 = 42 yr
On adding all three,
2 (A + B + C) = 40 + 38 + 42 = 120
⇒ A + B + C = 60
∴ A = (A + B + C) – (B + C) = 60 – 38 = 22 yr
Similarly,
B = (A + B) – A = 40 – 22 = 18 yr
C = (C + A) – A = 42 – 22 = 20 yr

Ryan’s Age = A = 22 Yrs
Karren’s Age = B = 18 Yrs
Chris’s Age = C = 20 Yrs

Explanation:
Using the Following Concept:
If the average of ‘N’ quantities is equal to ‘A’ when a quantity is removed the average becomes ‘B’. Then the value of the removed quantity is [N (A – B) + B].
Given that,
Number of players = N = 27, Difference in average = (A – B) = 1 cm
Old average = A = 162, New average = B = 162 – 1 = 161 cm

By the short trick approach, we get
[N (X – Y) + Y]
[27 (1) + 161] = [27 + 161] = 188 cm

Explanation:
According to the question, the average score of Ramey, Megan and Sherman is 63.
∴ Ryan's score = 63 + 30 = 93
Now,
Ramey's score = 93 – 15 = 78
Megan's score = 78 – 10 = 68
∴ Sherman's score = 63 × 3 – (78 + 68) = 43
∴ (Megan + Sherman)'s scores = 68 + 43 = 111

Explanation:
As per the question,
No. of hours Abhishek typed on Sunday = 50 / 30 = 5 / 3
No. of hours Abhishek typed on Monday = 50 / 20 = 5 / 2
Total hours of typing = 5 / 3 + 5 / 2 = 25 / 6
Total pages typed = 50 + 50 = 100
Average rate of typing = 100 / (25 / 6 ) = 6 x 4 = 24
Hence, James Gunn typed 24 pages per hour.

Explanation:
Given, the average price of a camlin pencil = ₹ 2
∴ Total price of 75 camlinpencils = 75 × 2 = ₹ 150
Let the price of a mont blanc pen = ₹ x
∴ Total price of 30 mont blanc pens = ₹ 30x
According to the question,
150 + 30x = 510
30x = 510 – 150 = 360
x = 360 / 30 = Rs 12
Required Average = \frac{Total PriceOf Pens}{NumberOf Pens}=\frac{30\times 12}{30}
Required Average = Rs 12