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

Explanation

First, find the price of one mango: Rs. 1517.25 ÷ 357 mangoes = Rs. 4.25 per mango (approximately)

Since you want to know the price of 49 dozen mangoes, convert 49 dozen to total mangoes: 49 dozen x 12 mangoes/dozen = 588 mangoes

Now, multiply the total mangoes by the price of one mango: 588 mangoes x Rs. 4.25/mango = Rs. 2500

Explanation

The relative speed of the two trains is the sum of their individual speeds, since they're moving in opposite directions: 62 km/h + 40 km/h = 102 km/h

Convert the relative speed from km/h to m/s: 102 km/h x (1000 m / 3600 s) = 28.33 m/s (approximately)

The time it takes for the trains to cross each other is given as 18 seconds.

The total distance covered by the trains during this time is the sum of their lengths. Let's call the length of the other train "x". Then, the total distance = 260 m + x

Since the relative speed is 28.33 m/s, the total distance can also be calculated as: Total distance = Relative speed x Time = 28.33 m/s x 18 s = 510 m

Equate the two expressions for total distance: 260 m + x = 510 m

Solve for x: x = 510 m - 260 m = 250 m

Explanation

A is 4 times as fast as B, so A's rate of work is 4 times B's rate of work.

Since A finishes the work in 45 days less than B, let's assume B takes x days to finish the work. Then A takes x - 45 days to finish the work.

Since A is 4 times as fast as B, A's rate of work is 4 times B's rate of work. So, A's time to finish the work is 1/4 of B's time.

We can set up an equation based on the above: x - 45 = (1/4)x

Solve for x: x - 45 = (1/4)x --> 4x - 180 = x --> 3x = 180 --> x = 60

So B takes 60 days to finish the work, and A takes 60 - 45 = 15 days to finish the work.

Since A and B work together, their combined rate of work is the sum of their individual rates. Let's find their individual rates.

B's rate = 1/60 (work done per day)

 A's rate = 1/15 (work done per day)

Combined rate = (1/60 + 1/15) = (1/60 + 4/60) = 5/60 = 1/12

So A and B together can complete the work in 12 days.

Explanation

Ali earns Rs. 7500 in 2 weeks.

Since there are 6 working days in a week, Ali works a total of 2 weeks x 6 days/week = 12 days.

Ali's daily earnings can be calculated by dividing his total earnings by the number of days he works: Rs. 7500 ÷ 12 days = Rs. 625 per day.

Since you asked for Ali's earnings in 2 days, we multiply his daily earnings by 2: Rs. 625 per day x 2 days = Rs. 1250.

Explanation

Since 12 pumps can empty the tank in 20 minutes, the rate at which they empty the tank is 1 tank / 20 minutes.

With 2 pumps out of order, we have 12 - 2 = 10 pumps left. Since the rate is directly proportional to the number of pumps, the rate of the remaining 10 pumps is:

10/12 × (1 tank / 20 minutes) = 1 tank / 24 minutes

So, the remaining 10 pumps will take 24 minutes to empty the tank.

Explanation

Explanation

Let the two-digit number be xy, where x is the tens digit and y is the units digit.
The sum of its digits is x + y.
The number is three times the sum of its digits, so we can write an equation: xy = 3(x + y).
Simplify the equation: 10x + y = 3x + 3y.
Rearrange the equation to get: 7x = 2y.
Now, if 45 is added to the number, the digits are reversed, so we can write another equation: xy + 45 = yx.
Simplify the equation: 10x + y + 45 = 10y + x.
Rearrange the equation to get: 9x = 9y - 45.
Divide both sides by 9 to get: x = y - 5.
Now we have two equations:

1. 7x = 2y

2. x = y - 5

Substitute the second equation into the first equation:
7(y - 5) = 2y
Expand and simplify:
7y - 35 = 2y
5y = 35
y = 7
Now that we have found y, substitute it back into one of the original equations to find x:
x = y - 5
x = 7 - 5
x = 2
So, the original number is 27.

Explanation

I=P×R×T

Principal amount (P) = 60,000

Rate of interest (R) = 9% per year

Time (T) = 3 years

Simple interest (SI) = (P x R x T) / 100

= (60,000 x 9 x 3) / 100

= 16,200

The total amount he repaid after 3 years is:

Principal + Interest = 60,000 + 16,200 = 76,200