Explanation

To evaluate this expression, we need to follow the order of operations (PEMDAS):

• Divide 3 by 1/3: 3 ÷ 1/3 = 3 × 3 = 9
• Subtract 9 from 9: 9 - 9 = 0
• Add 1 to 0: 0 + 1 = 1

So, the solution to the equation is 1.

Explanation

Since the sum of the angles in a triangle is always 180 degrees, and two of the angles are already 60 degrees each, the third angle can be found by subtracting the sum of the two known angles from 180:

180 - (60 + 60) = 180 - 120 = 60

So, the third angle is also 60 degrees, making the triangle an equilateral triangle.

Explanation

Since the student is 13th from the right, there are 12 students to their right.

And since they are 8th from the left, there are 7 students to their left.

To find the total number of students, you can add the number of students to their left and right, plus 1 (the student themselves):

7 (to the left) + 12 (to the right) + 1 (the student) = 20

So, there are 20 students in total.

Explanation

Since there are 8 mango trees, and the distance between each tree is 3 meters, the total distance between the first tree and the eighth tree would be:

7 gaps (between 8 trees) x 3 meters per gap = 21 meters

So, the distance between the first tree and the eighth tree is 21 meters!

Explanation

The logic is:

10 cats can catch 10 rats in 10 seconds

To catch 100 rats, the same 10 cats will take 100 seconds (since the rate of catching rats is the same)

Therefore, the number of cats required remains the same, i.e., 10

So, 10 cats can catch 100 rats in 100 seconds!

Explanation

3.4% can be written as a fraction by dividing by 100 (since percent means "per hundred"):

3.4 ÷ 100 = 34 ÷ 1000

So, 3.4% is equal to the fraction 34/1000.

Explanation

To find the percentage discount, first, calculate the amount of the discount:

Discount = Original price - Paid price

= Rs 600,000 - Rs 570,000

= Rs 30,000

Then, divide the discount by the original price and multiply by 100:

Percentage discount = (Discount ÷ Original price) × 100

= (Rs 30,000 ÷ Rs 600,000) × 100

= 5%

So, Mr. Rehman received a 5% discount on his car purchase.

Explanation

When the trains move in opposite directions, their relative speed is the sum of their individual speeds:

60 km/h + 40 km/h = 100 km/h

To convert this to meters per second, divide by 3600 (since there are 3600 seconds in an hour):

100 km/h ÷ 3600 = 27.78 m/s (approximately)

The total distance covered by the trains as they cross each other is the sum of their lengths:

140 m + 160 m = 300 m

Time = Distance ÷ Relative Speed

Time = 300 m ÷ 27.78 m/s ≈ 10.8 s

Explanation

600 units are made in 9 days with 20 machines.

To find the number of units made per day, divide 600 by 9: 600 ÷ 9 = 66.67 units per day.

Since there are 20 machines, the number of units made per day per machine is: 66.67 ÷ 20 = 3.33 units per day per machine.

Now, if we have 18 machines and want to produce units for 12 days, the total units that can be made are: 3.33 units per day per machine × 18 machines × 12 days = 720 units.

So, with 18 machines, the soap factory can produce 720 units in 12 days.

Explanation

The pattern in the series is as follows:

9 + 1 = 10

10 + 3 = 13

13 + 6 = 19

The next difference should be +9:

19 + 9 = 28

So, the correct answer is 28.