Numbers - Quiz

Let's say the number we are trying to find is x. We know that the number is multiplied by one-third of itself to get 192, so we can write the equation:

x * (1/3) * x = 192
Simplifying the left side of the equation, we get:

(1/3) * x^2 = 192
Multiplying both sides of the equation by 3, we get:

x^2 = 576
Taking the square root of both sides of the equation, we get:

x = 24
Therefore, the number we are looking for is 24.

 Let the integer x be such that x + x^2 = 272.

 This can be rewritten as x^2 + x - 272 = 0, which factors to (x + 17)(x - 16) = 0. 

Therefore, x = 16

x = (2/5)x + 45
x = (3/5)x + 45
x = 75 

 To find the unit digit in the product of the numbers 624, 708, 913, and 463, 
we can use the fact that the unit digit of a product is the same as the unit digit of each of the factors.

The unit digit of 624 is 4, the unit digit of 708 is 8, the unit digit of 913 is 3, and the unit digit of
 463 is 3. Therefore, the unit digit of the product of these numbers is the same as
 the unit digit of 4 * 8 * 3 * 3, which is equal to 8.

Therefore, the unit digit in the product (624 * 708 * 913 * 463) is 8. 

To find the number such that when 15 is subtracted from 7 times the number, the result is 10 more than twice the number, we can use the following steps:
Let the number be represented by the variable x.
Set up the equation 7x - 15 = 2x + 10.
Solve the equation to obtain 5x = 25, which simplifies to x = 5.
The required number is x, which is equal to 5.

Given:

x - y = 11
(x + y)/5 = 9
Add the two equations:

(6x + 4y)/5 = 20
6x + 4y = 100
Solve for x:

x = (100 - 4y)/6
We could have solved for x by substituting the value of y from the first equation into the second equation.
This would give us the equation:

x = 28
Substituting this value for x into the first equation, we would get:

y = 17
Therefore, the two numbers are x = 28 and y = 17.

Given:

x + y = 42
xy = 437
Find:

|x - y|
Substitute the first equation into the expression for |x - y| to get:

|x - y| = √((x + y)^2 - 4xy)
Substitute the given values for x + y and xy into this expression to get:

|x - y| = √((42^2) - 4(437)) = √(1764 - 1748) = √(16) = 4
Therefore, the absolute difference between the numbers is 4.

Given:

The ratio between a two-digit number and the sum of the digits of that number is 4:1
The digit in the unit's place is 3 more than the digit in the ten's place
Let the digit in the ten's place be x.
Then the digit in the unit's place is x + 3 and the sum of the digits is 2x + 3. 
The two-digit number can be expressed as:

10x + (x + 3) = 11x + 3
The ratio of the number to the sum of its digits is given by:

(11x + 3) / (2x + 3) = 4/1
Solve for x:

3x = 9
x = 3
Therefore, the two-digit number is 11x + 3 = 11(3) + 3 = 36.

In this approach, you first convert the units to the same type of mass measurement (1 metric tonne = 10 quintals), 

And then divide the number of quintals by the number of metric tons and multiply by 100 to express the result as a percentage.

The expression "40/(2 * 10)" simplifies to "4", and when this value is multiplied by 100%, the result is 200%. 

This shows that 40 quintals is equal to 200% of 2 metric tons.

Required difference = [3 ½ % of Rs.8400] – [3 1/3 % of Rs.8400]
= [(7/20-(10/3)]% of Rs.8400 =1/6 % of Rs.8400
= Rs. [(1/6)8(1/100)*8400] = Rs. 14