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

Four people live in a house.

There are 22 houses in one street.

To find the total number of people living in the street, multiply the number of people per house by the number of houses:

4 people/house × 22 houses = 88 people

So, 88 people live in the street.

Explanation

To find the number of lawns completed in 10 hours, we can set up a proportion:

2 hours / 3 lawns = 10 hours / x lawns

We can then cross-multiply and solve for x:

2x = 3 × 10

2x = 30

x = 30/2

x = 15

So, in 10 hours, 15 lawns will be completed.

Explanation

To find the smallest ratio, we need to simplify the fraction 0.35/0.65.

First, convert the decimals to fractions:

0.35 = 35/100 = 7/20

0.65 = 65/100 = 13/20

Now, divide the fractions:

(7/20) ÷ (13/20) = 7/13

So, the smallest ratio is 7/13.

Explanation

If 2/3 of the men do not attend the mess, that means only 1/3 of the men are attending the mess.

Since the provision is for 30 days for the entire group, the food will now last three times as long, since only one-third of the group is consuming it.

So, the food will last for 30 x 3 = 90 days.

Explanation

To find |f(1)|, we need to evaluate the function f(x) = -3(x^2) - 2(x) + 1 at x = 1.

f(1) = -3(1^2) - 2(1) + 1

= -3(1) - 2(1) + 1

= -3 - 2 + 1

= -4

Now, we need to find the absolute value of f(1):

|f(1)| = |-4| = 4

Explanation

To find the original price, we need to remove the GST amount from the inclusive price.

Price including GST = Rs. 945

GST percentage = 5%

First, convert the GST percentage to a decimal: 5% = 0.05

Then, divide the price including GST by (1 + GST decimal):

Rs. 945 ÷ (1 + 0.05) = Rs. 945 ÷ 1.05 = Rs. 900

Explanation

To calculate the percentage of discount, you can use the following formula:

percentage discount = (original price – new price) / original price * 100%

In this case, the original price is 0.62 and the new price is 0.42. So, the calculation would be:

percentage discount = (0.62 – 0.42) / 0.62 * 100% = 0.2 / 0.62 * 100% = 0.3225806452 * 100% = 32.26% ~= 32%

Therefore, the actual percentage of discount is 32%.

Explanation

Price inclusive of GST = 6480

GST percentage = 8%

First, convert the GST percentage to a decimal:

8% = 0.08

Now, divide the price inclusive of GST by (1 + GST decimal):

6480 ÷ (1 + 0.08) = 6480 ÷ 1.08 = 6000

So, the original price of the bicycle is 6000.