Explanation

Let's break it down step by step:

Let the principal amount be P.

According to the problem, the amount becomes 3 times itself in 20 years, so the interest earned is 2P (since 3P = P + 2P).

The simple interest formula is: Interest = (Principal × Rate × Time)/100

We know that Interest = 2P and Time = 20 years. Let's denote the rate as R.

So, 2P = (P × R × 20)/100

Simplifying, we get: R = 10%

Now, let's find the time it takes for the amount to become double (i.e., interest = P):

P = (P × 10 × Time)/100

Time = 10 years

Explanation

Given:

Capacity = 50000 litres = 50 cubic meters (since 1 cubic meter = 1000 litres)

Length (l) = 2.5 m

Depth (h) = 10 m

Let's use the formula for the volume of a cuboid:

Volume = length × breadth × height

50 = 2.5 × breadth × 10

Now, solve for breadth (b):

50 = 25b

b = 50/25

b = 2 m

Explanation

To find the value of 39/26:

39/26 = 1.5

= 3/2

Explanation

Given |n - 2| = 10:

We have two cases:

1. n - 2 = 10 => n = 12

2. n - 2 = -10 => n = -8

The sum of the two possible values of n:

12 + (-8) = 4

Explanation

A circle can have an infinite number of tangents.

Since a circle is defined as a set of points equidistant from a fixed point,

And each point on the circle can have a tangent line, there are infinitely many possible tangent lines. 

Explanation

To find the square of the distance between two points $A(x_1, y_1)$ and B(x2​,y2​):

AB^2=(x2​−x1​)^2+(y2​−y1​)^2 $$= (3 - 4)^2 + (5 - (-1))^2 = (-1)^2 + (6)^2 = 1 + 36 = 37$$

=(−1)^2+(6)^2

=1+36

$$=37$$

Explanation

Let's examine the sequence:

19, 26, 33, 40, 47, 53

The differences between consecutive terms:

26 - 19 = 7

33 - 26 = 7

40 - 33 = 7

47 - 40 = 7

53 - 47 = 6

Given the pattern of differences is +7 consistently except for the last step:

The sequence follows a pattern of adding 7, but 53 - 47 = 6 breaks this pattern.

So, 53 is the odd one in the sequence.

Explanation

The sequence shows factorials: 1!, 1!, 2!, 3!, 4!, so next is 5! = 120.

Explanation

. Starts facing North, moves 7 km North.  

2. Turns West, moves 2 km.  

3. Turns South, moves 4 km → Now he's (7 - 4) = 3 km North from start.  

4. Turns West again, moves another 2 km → Total 4 km West.

So, from starting point, he's 3 km North and 4 km West.

Use Pythagoras theorem to find distance from start:

Distance = √(3² + 4²) = √(9 + 16) = √25 = 5 km

Explanation

1. Original total age of 13 boys:

2. New average after 2 boys join = 13 + 2 = 15 years

Total boys = 13 + 2 = 15 boys

So, the total age of the 15 boys = 15×15=225 years

3. Sum of ages of the 2 new boys =