Explanation

1. Average income of A and B is 50000, so their total income is:

2 x 50000 = 100000

2. Average income of B and C is 60000, so their total income is:

2 x 60000 = 120000

3. Average income of A and C is 55000, so their total income is:

2 x 55000 = 110000
Now, let's analyze the situation:

- A's income + B's income = 100000 ... (1)

- B's income + C's income = 120000 ... (2)

- A's income + C's income = 110000 ... (3)

We can add (1) and (3), and subtract (2) from the result:
(100000 + 110000) - 120000 = 90000
Simplifying this, we get:
190000 - 120000 = 70000
Now, divide by 2:
70000 / 2 = 35000
Now, add B's income and C's income (equation 2):
35000 + C's income = 120000
Subtract 35000 from both sides:
C's income = 85000
Now, subtract C's income from equation (3):
A's income + 85000 = 110000
Subtract 85000 from both sides:
A's income = 25000
Now, subtract A's income from equation (1):
25000 + B's income = 100000
Subtract 25000 from both sides:
B's income = 75000 - 25000
B's income = 55000
So, B's income is 55000.

Explanation

- The player's average runs in 10 innings is 33, so the total runs scored by the player in 10 innings is:

33 x 10 = 330 runs

- To increase the average by 3, the new average will be:

33 + 3 = 36

- Since the player has already played 10 innings, the total number of innings now becomes 11 (including the next innings).

- Let x be the runs scored in the next innings. The new total runs will be:

330 + x

- The new average is 36, so we can set up the equation:

(330 + x) / 11 = 36

- Solve for x:

330 + x = 396
x = 66
So, the player needs to score 66 runs in the next innings to increase the average by 3.

Explanation

The average marks of four subjects is 120, so the total marks are:

120 x 4 = 480

If 33 was misread as 13, that means the actual total marks should be:

480 - 13 + 33 = 500

Now, let's calculate the correct average:

Correct average = Total marks / Number of subjects

= 500 / 4

= 125

Explanation

7*70 = 490 kg - total weight of 7 people

80 - 60 = 20 kg less

(490 -20)/7 ≈ 67.14 kg - new average weight ANSWER

Explanation

Let the first number be = 6xSecond number = 3xand the third number = 2xAccording to the question 6x + 3x + 2x = 154 × 3or 11x = 154 × 3Required difference = 6x – 2x = 4x = 4 × 42 = 168

Explanation

The sum of all odd numbers between 1 and 100 is 50^2=2500

The sum of all even numbers between 2 and 100 is 50^2+50=2550

The total of 1 to 100 natural numbers is 2500+2550

5050

The average of the first 100 numbers is 5050 / 100 = 50.50

Explanation

Total cartons = 5 + 8 = 13

Total cost = 105 + 155 = 260

Total items = 13 x 5 = 65

Average price per item = Total cost / Total items = 260 / 65 = 4

Explanation

To calculate the total number of people:

$$text{Total number of people} = (text{Your position from the start}) + (text{Your position from the end}) - 1$$

Substitute the values:

$$6+6-1=11$$

Explanation

We are given:

• 4 boxes with weights: 20 kg, 30 kg, 50 kg, and 70 kg.

We need to determine which total weight cannot be made by combining these boxes.

Let's check the combinations:

1. 20 + 30 + 50 + 70 = 170 kg
2. 20 + 30 + 50 = 100 kg
3. 20 + 30 + 70 = 120 kg
4. 20 + 50 + 70 = 140 kg
5. 30 + 50 + 70 = 150 kg

Now check if 160 kg can be made:

• The possible combinations do not result in 160 kg.

Explanation

There are:

• 8 red toys
• 6 green toys
• 7 blue toys

The total number of toys is:

$$8+6+7=21\text{toys}$$

We are asked to find the probability that the toy picked is neither red nor green, which means it must be blue.

The number of blue toys is 7, so the probability is:

17​/21=1/3​