Explanation

7x - 1 = 4x + 8

Add 1 to both sides:

7x = 4x + 9

Subtract 4x from both sides:

3x = 9

Divide both sides by 3:

x = 3

So, the value of x is 3.

Explanation

From equation (1), we can write:

2 = 10^0.3010

Now, take log base 2 on both sides:

log2 2 = log2 (10^0.3010)

1 = 0.3010 log2 10

Now, divide both sides by 0.3010:

log2 10 = 1/0.3010

= 100/30.10

= 1000/301

Explanation

When 52416 is divided by 312, the quotient is 168. To find the quotient when 52.416 is divided by 0.0168, we can set up a proportion:

52416 ÷ 312 = 168

52.416 ÷ 0.0168 = x

We can then cross-multiply and solve for x:

x = (52.416 × 312) ÷ 0.0168

x = 3120

So, the quotient is 3120.

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 calculate David's average marks, we need to add up all his marks and divide by the number of subjects:

English: 76

Mathematics: 65

Physics: 82

Chemistry: 67

Biology: 85

Total marks: 76 + 65 + 82 + 67 + 85 = 375

Number of subjects: 5

Average marks: 375 ÷ 5 = 75

So, David's average marks are: 75

Explanation

Find the area of the rectangular lawn:

Area = Length x Breadth = 80m x 60m = 4800 square meters

Since there are two roads, one parallel to the length and one parallel to the breadth, we need to find the area of each road:

Road parallel to length:

Area = Length x Width = 80m x 10m = 800 square meters

Road parallel to breadth:

Area = Breadth x Width = 60m x 10m = 600 square meters

However, the problem states that the roads are running in the middle of the lawn, which means they intersect. To avoid double-counting the intersection area, we need to subtract it:

Intersection Area = Width x Width = 10m x 10m = 100 square meters

Now, add the areas of both roads and subtract the intersection area:

Total Road Area = (800 + 600) - 100 = 1300 square meters

Finally, calculate the cost of gravelling the roads at Rs. 30 per square meter:

Cost = Total Road Area x Rate = 1300 x 30 = Rs. 39000

Explanation

1. We are given that 1/2 inch is equal to 12 kilometers.

2. We want to find the distance in kilometers for 5-2/3 inches. First, let's convert the mixed number to an improper fraction:

5-2/3 = 17/3 inches

3. Now, let's set up a proportion using the given conversion factor:

(1/2 inch) / 12 km = (17/3 inches) / x km

4. We can then cross-multiply and solve for x:

(1/2) × x = (17/3) × 12
x = (17/3) × 12 / (1/2)
x = (17/3) × 24
x = 136 km
So, the distance in kilometers is 136 km.

Explanation

Let's calculate the new length and width of the picture:

Original length (L) = 9 cm

Original width (W) = 5.5 cm

Enlargement ratio = 7:5

New length (L') = (7/5) × L = (7/5) × 9 = 12.6 cm

New width (W') = (7/5) × W = (7/5) × 5.5 = 7.7 cm

So, the new length and width of the picture are:

7.7 cm by 12.6 cm

Explanation

Principal (P) = 65000

Interest Rate (R) = 3% = 0.03

Interest Amount (I) = 68900 - 65000 = 3900 (since the interest amount is the total amount paid minus the principal)

We can use the formula: I = P × R × T

Rearranging the formula to solve for T, we get:

T = I / (P × R)

= 3900 / (65000 × 0.03)

= 3900 / 1950

= 2 years

So, it takes 2 years for the interest to become 68900.

Explanation

Current sum of ages = 100 years

5 years ago, their ages were in the ratio of 2:1. Let's call the father's age 5 years ago "2x" and the son's age 5 years ago "x".

We know that 5 years ago, their sum of ages was:

2x + x = 3x

Since the current sum of ages is 100, we can set up an equation:

(2x + 5) + (x + 5) = 100

Combine like terms:

3x + 10 = 100

Subtract 10 from both sides:

3x = 90

Divide by 3:

x = 30

So 5 years ago, the father's age was 2x = 60 and the son's age was x = 30.

Now, let's find their ages after 10 years:

Father's age = 60 + 5 + 10 = 75

Son's age = 30 + 5 + 10 = 45

The ratio of their ages after 10 years is:

75:45 = 5:3