Explanation

9/11 + 5/7 = 3/2

Explanation

3x-54 = 36

3x = 90

x = 30

Explanation

To find the time taken, subtract the departure time from the arrival time.

Departure time: 22:55

Arrival time: 06:05 (next day)

First, convert the times to a 24-hour clock:

Departure time: 22:55

Arrival time: 06:05

Subtract the departure time from the arrival time:

06:05 - 22:55 = 7 hours 10 minutes

Therefore, the time taken for the journey is 7 hours 10 minutes.

Explanation

Euclid Considered the "father of geometry"

He was an ancient Greek mathematician active as a geometer and logician.

Known for: The Elements, Optics, Data

Died: Alexandria, Egypt

Last updated question  18-02-2026

Explanation

In the first y hours, the carpenter lays xy bricks.

In the 2y hours thereafter, he lays (x/2)(2y) = xy bricks.

Altogether, that's xy + xy = 2xy bricks.

Explanation

Let's calculate the price of the printer after 3 years, considering an annual depreciation of 4%:

Year 1:

Depreciation = 4% of Rs. 150000 = Rs. 6000

Price after 1 year = Rs. 150000 - Rs. 6000 = Rs. 144000

Year 2:

Depreciation = 4% of Rs. 144000 = Rs. 5760

Price after 2 years = Rs. 144000 - Rs. 5760 = Rs. 138240

Year 3:

Depreciation = 4% of Rs. 138240 = Rs. 5529.60

Price after 3 years = Rs. 138240 - Rs. 5529.60 = Rs. 132710.40

Rounding to the nearest whole number, the price of the printer after 3 years is:

Rs. 132710

Explanation

1.  The last place team (8th position) gets Rs. 4000.

2. The prize money increases by the same amount for each higher position.

3. There are 8 teams, so we need to find the increase in prize money per position.

4. Let's assume the increase per position is x.

5. The 7th position team gets Rs. 4000 + x = ?

6. The 6th position team gets Rs. 4000 + 2x = ?

7. ...

8. The 1st position team gets Rs. 4000 + 7x = ?

We know the total prize money is Rs. 60,000. Let's add up the prize money for each position:
Rs. 4000 + (Rs. 4000 + x) + (Rs. 4000 + 2x) + ... + (Rs. 4000 + 7x) = Rs. 60,000
Combine like terms:
8(Rs. 4000) + 28x = Rs. 60,000
Simplify:
Rs. 32,000 + 28x = Rs. 60,000
Subtract Rs. 32,000 from both sides:
28x = Rs. 28,000
Divide by 28:
x = Rs. 1000
Now we know the increase per position is Rs. 1000.
The 1st position team gets:
Rs. 4000 + 7x = Rs. 4000 + 7(Rs. 1000) = Rs. 4000 + Rs. 7000 = Rs. 11,000

Explanation

The place value of 9 in 0.06945 is 9/10000, since the 9 is in the ten-thousandths place.

Here's how the place values work in this number:

•  0 is in the ones place
•  0 is in the tenths place
•  6 is in the hundredths place
•  9 is in the thousandths place
•  4 is in the ten-thousandths place
•  5 is in the hundred-thousandths place

So, the 9 is in the thousandths place, making its place value 9/10000.

Explanation

Since the population growth is exponential, the population P can be modeled as:

P = P0 x (1 + r)^t

where P0 is the initial population, r is the growth rate, and t is the time (in years).

Given that the initial population P0 = 20 and the population grew to 25 after 2 years, we can find the growth rate r:

25 = 20 x (1 + r)^2

Dividing both sides by 20:

1.25 = (1 + r)^2

Taking the square root:

1 + r = √1.25 = 1.125

Subtracting 1 from both sides:

r = 0.125

Now we can write the exponential growth function:

P = 20 x (1 + 0.125)^t

P = 20 x (1.25)^t

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.