Explanation

5/5 = 1

1 × 5/10 = 1/2

1/2 × 5/15 = 1/6

1/6 × 5/20 = 1/24

1/24 × 5/25 = 1/120

Explanation

3 + 5 = 8

3 + 4 = 7

2 + 4 = 6

1 + 8 = 9

Explanation

To calculate the total number of handshakes:

Each person shakes hands with 9 others.

There are 10 people, so it seems like there would be 10 x 9 = 90 handshakes.

However, this counts each handshake twice (once for each person involved).

To correct this, divide the total by 2:

90 / 2 = 45

Explanation

To evaluate the expression, follow the order of operations:

(2²)³ = (2 × 2)³

= 4³

= 4 × 4 × 4

= 64

Explanation

Market price = x

Price after 5% increase = x + 0.05x = 1.05x

Sales tax = 12% of x = 0.12x

Total price paid by customer = 1.05x + 0.12x = 1.17x

Given that the total price paid is Rs. 4680:

1.17x = 4680

x = 4680 / 1.17

x = 4000

Explanation

The quadratic equation whose roots are reciprocal of:

2x2 + 5x + 3 = 0 can be obtained by replacing x by 1/x.

Hence, 2(1/x)2 + 5(1/x) + 3 = 0

=> 3x^2 + 5x + 2 = 0

Explanation

We can write % as 1/100 so.

142.5/100 = 1.425

Explanation

 My son’s Uncle is my Brother.

Therefore, My brother’s father is my father.

Explanation

The average weight of A, B, and C is 45 kg, so the total weight is 45 x 3 = 135 kg.

The average weight of A and B is 40 kg, so their total weight is 40 x 2 = 80 kg.

The average weight of B and C is 43 kg, so their total weight is 43 x 2 = 86 kg.

Now, let's find the weight of B:

Subtract the weight of A from the total weight of A and B: 80 kg - A = B

Subtract the weight of C from the total weight of B and C: 86 kg - C = B

Since the total weight of A, B, and C is 135 kg, we can set up the equation:

A + B + C = 135

Substituting the expressions for B from steps 1 and 2, we get:

(80 kg - B) + B + (86 kg - B) = 135

Simplifying the equation, we get:

166 kg - B = 135

Subtracting 166 kg from both sides:

-31 kg = -B

Dividing both sides by -1:

B = 31 kg

Therefore, the weight of B is 31 kg.

Explanation