Explanation

Step 1: Let's denote the two numbers as x and y.
We have two equations:

1. x + y = 28

2. x - y = 4

Step 2: Solve the system of equations.
Adding the two equations eliminates y:
(x + y) + (x - y) = 28 + 4
2x = 32
Step 3: Solve for x.
x = 32 / 2
x = 16
Step 4: Solve for y.
Substitute x into one of the original equations:
16 + y = 28
y = 28 - 16
y = 12
Step 5: Identify the correct pair of numbers.
The numbers are 16 and 12.

Explanation

Sum of A,B,C,D = 45 * 4 = 180  

New average after E = 49 with 5 persons → Total sum = 49 * 5 = 245  

E's age = 245 - 180 = 65 years

Explanation

The mean proportional between two numbers a and b is √(ab).

So, √(2 × 8) = √16 = 4.

Explanation

Casey can carry 4 boxes per trip.

Total boxes = 33

Number of trips = 33 ÷ 4 = 8.25

Since he can’t make a fraction of a trip, he needs 9 trips.

Explanation

To find the average:

(25 + 20 + 17 + 19) ÷ 4  

= 81 ÷ 4  

= 20.25

Explanation

Let's find the third number:

Average = (Sum of numbers) / 3

65 = (60 + 75 + x) / 3

65 × 3 = 60 + 75 + x

195 = 135 + x

x = 195 - 135

x = 60

Explanation

- 3 pointers point 3 walls in 3 minutes.

- So, 1 pointer points 1 wall in 3 minutes.

Now, we want to know how many pointers are needed to point 27 walls in 9 minutes.

Since 1 pointer points 1 wall in 3 minutes, in 9 minutes (which is 3 times longer), 1 pointer can point:

1 wall × 3 = 3 walls.

To point 27 walls in 9 minutes:

Number of pointers needed = Total walls / Walls per pointer = 27 / 3 = 9 pointers.

Explanation

We need to divide Rs. 712,000 between two towns with populations 1,800 and 1,500, in proportion to their population.

Step 1: Total Population  

1800 + 1500 = 3300

Step 2: Share per person  

712,000 ÷ 3300 = Rs. 215.76 approx.

Step 3: Each town’s share  

- Town A (1800 people):  

  1800 × 215.76 = Rs. 388,363 approx.  

- Town B (1500 people):  

  1500 × 215.76 = Rs. 323,636 approx.

Explanation

In a knockout tournament, each match eliminates one team. To decide a single winner from n teams, we must eliminate (n − 1) teams.

Here, n = 23  

So, number of matches needed = 23 − 1 = 22

Explanation

If Bastion is 16th from the front and 16th from the back, it means there are 15 people ahead of him and 15 people behind him.

So, total people in line =  

15 (in front) + 1 (Bastion) + 15 (behind) = 31