Explanation

Hassan borrowed Rs. 5000 for 5 years.

He paid an extra Rs. 500, which means he paid a total of Rs. 5000 (principal) + Rs. 500 (interest) = Rs. 5500.

Since he paid Rs. 500 as interest for 5 years, we can calculate the interest rate per annum (per year) as follows:

Interest = Rs. 500

Time = 5 years

Simple Interest (SI) = (Principal x Rate x Time) / 100

500 = (5000 x Rate x 5) / 100

Now, let's solve for Rate (interest rate per annum):

Rate = (500 x 100) / (5000 x 5)

= 2%

So, Hassan pays 2% interest per annum.

Explanation

Let the two numbers be $x$ and $y$, where $x > y$.

We are given:

$$x+y=40\text{(1)}$$$$x - y = 4 quad text{(2)}$$

Adding equations (1) and (2):

2x=44⟹x=22

Subtracting equation (2) from (1)

$$2y = 36 implies y = 18$$

The numbers are 22 and 18.
The ratio of the numbers is:

x​/y=22​/18

=11/9​

Explanation

(1+1/x) (1+1/x+1) (1+1/x+2) (1 + 1/x + 3)

Simplify each term:

(x+1)/x * (x+2)/x * (x+3)/x * (x+4)/x

Multiply the numerators and denominators:

(x+1)(x+2)(x+3)(x+4) / x^4

Expand the numerator:

x^4 + 10x^3 + 35x^2 + 50x + 24

Divide by x^4:

1 + 10/x + 35/x^2 + 50/x^3 + 24/x^4

Now, simplify the expression:

Combine like terms:

x + 4/x

Explanation

Let's assume the cost of the bike is x. Then, the cost of the car is 400% greater than the cost of the bike, which means the cost of the car is x + 400% of x = x + 4x = 5x.

The total cost of 5 cars and 10 bikes is:

5(5x) + 10x = 25x + 10x = 35x

The increase in cost is:

5 cars: 15% of 5(5x) = 0.15(25x) = 3.75x

10 bikes: 20% of 10x = 0.20(10x) = 2x

Total increase = 3.75x + 2x = 5.75x

The percentage increase is:

(5.75x / 35x) × 100 = (575 / 3500) × 100 = 16 3/7%

Explanation

Given,
220% of X = 44
Or, X = 20
Thus,
44% of 20

Explanation

To find the percentage of the second number to the first, divide the second by the first and multiply by 100:

(1.2x / 1.6x) × 100 = (12/16) × 100 = 75%

Explanation

0.009/x = 0.01

To isolate x, we can divide both sides by 0.009, which gives us:

1/x = 0.01/0.009

1/x = 1.111 (approximately)

Now, take the reciprocal of both sides:

x = 1/1.111

x ≈ 0.9

So, the value of x is approximately 0.9.

Explanation

Let the smaller number be 3x and the larger number be 5x, since their ratio is 3:5.

When 9 is subtracted from each number, the new numbers are 3x - 9 and 5x - 9.

The ratio of these new numbers is 12:23, so we can set up the equation:

(3x - 9) / (5x - 9) = 12/23

Cross-multiplying and simplifying the equation, we get:

69x - 207 = 60x - 108

Solving for x, we get:

9x = 99

x = 11

So, the smaller number is 3x = 3(11) = 33.

Explanation

3889 + 12.952 - X = 3854.002

First, combine the constants on the left side:

3901.952 - X = 3854.002

Now, subtract 3854.002 from both sides:

47.95 - X = 0

Subtract 47.95 from both sides:

-X = -47.95

Multiply both sides by -1:

X = 47.95

Explanation

Volume of iron =π(R2−r2)×h

=π(42−32)×21

=722​×(16−9)×21

=462cm2

Weight =10008×462​kg=3.696kg