Robert Bosch Averages Quiz-2

Explanation:
Total weight of 21 boys = 64 × 21 = 1344 kg

Given that if the weight of the teacher was added, the average increased by one kg
∴ Total weight along with the teacher = 65 × 22 = 1430 kg

Now, teacher's weight = 1430 – 1344 = 86 Kg

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

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

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

Explanation:
Let the number of subjects be 'N' and average marks be 'X'.
Then, total marks = NX
Again (N + 1)(X – 1) = (NX – 40) + (23 + 25)
⇒ X – N = 9 ….. (1)
Further (N + 2)(X + 1) = (NX – 40) + (23 + 25) + 57
⇒ NX + 2X + N + 2 = NX + 65
⇒ 2X + N = 63 .... (2)
Solving equations (1) and (2), we get
N = 15 and X = 24.

Explanation:
From the facts provided, it is clear that the south Indian couple's and the other member's average ages are equal because adding or subtracting their ages has no effect on the group's average.
We can find the average age of the couple and number of persons by applying the Hit & Trial method.
Let’s take option B which is 20, 27.
∴ Average age of the party members,
= \frac{540}{27}=20
We can confirm it further by putting it in the eq. as follows,
\frac{Total Age - (Total Age of Couple)}{Remaining No. Of Guests}=OldAge(Remain Unchanged)
\frac{540 - (20\times2)}{27-2}= 20 => L.H.S = R.H.S

Explanation:
Total annual income = Expenditure + Savings
= (4 × 2570 + 3 × 2490 + 5 × 3030) + 5320
= (10280 + 7470 + 15150) + 5320
= 32900 + 5320 = 38220

∴ Required average monthly income,
\frac{38220}{12} = 3185Rs

Explanation:
Total annual income = Expenditure + Savings
= (4 × 1800 + 8 × 2000) + 5600
= (7200 + 16000) + 5600
= 23200 + 5600 = Rs. 28800
∴ Required average monthly income,
\frac{28800}{12} = 2400Rs

Explanation:
Total age of 36 students = 14 × 36 = 504 years
Given that when teacher's age is included the average increases by one
∴ Total age along with the teacher = 15 × 37 = 555 years
Now, the teacher's age = 555 – 504 = 51 years

Explanation:
Total age of 12 players = 12 × 32 = 384 years
Given that if the age of one player is added, the average decreases by one year
∴ Total age of 13 players = 13 × 31 = 403 years
Now, age of new player = 403 – 384 = 19 years

Explanation:
The average age of the boys = 14 years
The sum of ages of the boys = 14 × 32 = 448 years
The average age of the girls = 13 years
The sum of ages of the girls = 13 × 28 = 364 years
The sum of ages of the boys and the girls = 448 + 364 = 812 years
Total students in the class = 32 + 28 = 60
Required Average, \frac{812}{60} = 13.53 Years

Explanation:
Given, average weight of 12 water bottles = 1.8 kg
∴ Total weight of 12 water bottles = 12 × 1.8 = 21.6 kg
If addition of another new water bottle reduces the average weight by 50 g.
∴ Average weight of 13 water bottles = 1.8 kg – 50 g = 1.75 kg
∴ Total weight of 13 water bottles= 13 × 1.75 = 22.75 kg
Now, weight of the new water bottle = 22.75 – 21.6 = 1.15 kg