Test: Averages - 1 - UCAT MCQ

Total weight of the 25 boys = Average weight of 25 boys x Number of boys = 48 kg x 25 = 1200 kg

Total weight of the entire class = Average weight of the entire class x Number of students = 45 kg x 40 = 1800 kg

Total weight of the 15 girls = Total weight of the entire class - Total weight of the 25 boys = 1800 kg - 1200 kg = 600 kg

Average weight of the 15 girls = Total weight of the 15 girls / Number of girls = 600 kg / 15 = 40 kg

Therefore, the average weight of the 15 girls in the class is 40 kg. The correct answer is option (c) 40 kg.

Since,The average temperature of W,T,and F = 20°C

So,The total temperature of W + T + F = 3 × 20°C

⇒ W + T + F = 60°C ——(1)

Again,The average temperature of T,F and S =24°C

So,T + F + S = 3 × 24°C

⇒ T + F + S = 72°C——(2)

And Temperature on Saturday =27°C

So,S = 27°C——(3)

Subtracting equation (3) from (2),we get.

T + F + S - S = 72°C - 27°C

⇒ T + F = 45°C—-(4)

Now, Subtracting equation (4) from (1)

(W + T + F) - (T + W) = 60°C - 45°C

⇒ W + T + F - T - F = 15°C

⇒ W = 15°C

Hence, the temperature on Wednesday = 15°C

Initially, the average monthly salary of 12 workers and 3 managers was Rs. 600. This means the total salary for all 12 workers and 3 managers combined was 15 * Rs. 600 = Rs. 9,000.

One of the managers had a salary of Rs. 720. This means the total salary for the remaining 11 workers and 2 managers was Rs. 9,000 - Rs. 720 = Rs. 8,280.

Now, we are told that when the new manager replaces the previous manager, the average salary of the team drops to Rs. 580. We can set up the equation:

(8,280 + x) / 15 = 580

Here, 'x' represents the salary of the new manager. We need to solve this equation to find the value of 'x'.

To solve the equation, we first multiply both sides by 15:

8,280 + x = 580 * 15
8,280 + x = 8,700

Next, subtract 8,280 from both sides:

x = 8,700 - 8,280
x = 420

Therefore, the salary of the new manager is Rs. 420.

The correct answer is (b) Rs. 420.

We are given that the average wage of the worker during a fortnight (15 consecutive working days) was Rs. 90 per day.

During the first 7 days, the average wage was Rs. 87 per day. This means the total wage for the first 7 days was 7 * Rs. 87 = Rs. 609.

During the last 7 days, the average wage was Rs. 92 per day. This means the total wage for the last 7 days was 7 * Rs. 92 = Rs. 644.

Now, to find the worker's wage on the 8th day, we need to find the total wage for all 15 days and subtract the wages for the first 7 and last 7 days.

Let 'x' be the worker's wage on the 8th day.

Total wage for all 15 days = 15 * Rs. 90 = Rs. 1350

Total wage for the first 7 days = Rs. 609

Total wage for the last 7 days = Rs. 644

So, we have the equation:

Rs. 609 + Rs. x + Rs. 644 = Rs. 1350

Rs. x = Rs. 1350 - Rs. 609 - Rs. 644

Rs. x = Rs. 97

Therefore, the worker's wage on the 8th day was Rs. 97.

The correct answer is (d) Rs. 97.

We are given that the average of 5 quantities is 6. This means the sum of these 5 quantities is 5 x 6 = 30.

We are also given that the average of 3 of those 5 quantities is 8. This means the sum of these 3 quantities is 3 x 8 = 24.

To find the sum of the remaining two quantities, we subtract the sum of the 3 quantities from the sum of all 5 quantities:

Sum of remaining two quantities = Sum of all 5 quantities - Sum of 3 quantities
Sum of remaining two quantities = 30 - 24 = 6

To find the average of the remaining two quantities, we divide the sum of the remaining two quantities by 2:

Average of remaining two quantities = Sum of remaining two quantities / 2
Average of remaining two quantities = 6 / 2 = 3

Therefore, the average of the remaining two quantities is 3.

The correct answer is (c) 3.

The total age of the original group is 5 x 25 = 125 years.
After adding the new friend, the total age becomes 125 + 30 = 155 years.
The new average age is 155 / 6 = 26.5 years.

The total weight of the group is 10 x  60 = 600 kg.
After correcting the weight of the individual, the total weight becomes 600 - 70 + 50 = 580 kg.
The new average weight is 580 / 10 = 58 kg.

The total salary of the group is 3000 x N, where N is the number of employees.
If we subtract the salary of the manager ($5,000), the total salary of the remaining employees is 3000 x (N - 1).
The average salary of the remaining employees is (3000 x (N - 1)) / (N - 1)
= $2,000.

The sum of the 10 numbers is 10 x 20 = 200.
After excluding one number, the sum becomes 9 x 18 = 162.
The excluded number is 200 - 162 = 38.
Therefore, the excluded number is 32.

The sum of the three numbers is 3 x 12 = 36.
If we subtract the given numbers (8 + 16) from the sum, we get the third number: 36 - (8 + 16) = 12.
Therefore, the third number is 6.