A number which is formed by two digits is 3 times the sum of the digits. While interchanging the digits it is 45 more than the actual number. Find the number.

The gas mileage M (s), in miles per gallon, of a car traveling s miles per hour is modeled by the function below, where  .

According to the model, at what speed, in miles per hour, does the car obtain its greatest gas mileage?

Note:
We could have also used the first derivative test to find the local
maxima. We need to find critical points and then check whether the
function is increasing or decreasing on either side of the critical
point. If the function is increasing , i. e .,  on the left side
and the function is decreasing, i. e .,  on the right hand side, then we say that  is a local maxima.

Given a rectangle ABCD, where AB = (4y-z) cm, BC = (y+4) cm, CD = (2y+z+8) cm, DA = 2z cm. Find y and z

Find the volume of a right circular cylinder of length 80 cm and diameter of the base 14 cm.
 

Find the area of the polygon in the given picture, cm, 

A man bought 3 paise and 5 paise denomination stamps for Rs 1.00. In total he bought 22 stamps. Find out total number of 3 paise stamps bought by him.

A ball pen costs Rs 3.50 more than pencil. Adding 3 ball pens and 2 pencils sum up to Rs 13. Taking y and z as costs of ball pen and pencil respectively. Write down 2 simultaneous equations in terms of y and z which satisfy the above statement. Find out the values of y and z.

In a town there are 2 brothers namely Anand and Suresh. Adding 1/3 rd anand’s age and suresh age would sum up to 10. Also adding Anand’s age together with 1⁄2 of suresh age would sum up to 10. Find Anand and Suresh ages.

From a cylindrical wooden log of length 30 cm and base radius 72 cm, biggest cuboid of square base is  made. Find the volume of wood wasted?

Find the area of the figure.
.

The system of equations above is graphed in the xy -plane. At which of the following points do the graphs of the equations intersect?

Note:
We can solve the equations by other methods too, but the method of substitution is most suitable here. Also, instead of solving
 by middle term factorisation, we could also use the quadratic formula, which is given by

Where the standard form of equation is 

Find the area of an isosceles trapezium ABCD, if the parallel sides are 6cm and 14 cm, its non parallel sides is 5cm each.

 and  Solve by using the elimination method.

The sides of a parallelogram are 12cm and 8cm. one of the diagonal is 10cm long. If d is the length of the other diagonal, then which of the following is correct?

Cylindrical vessel of diameter 9 cm has some water in it. A cylindrical iron piece of diameter 6 cm and height 4.5 cm is dropped in it. After it was completely immersed, find the rise in the level of water.

During mineral formation, the same chemical compound can be come different minerals depending on the temperature and pressure at the time of formation. A phase diagram is a graph that shows the conditions that are needed to form each mineral. The graph above is a portion of the phase diagram for aluminosilicates, with the temperature t , in degrees
Celsius  , on the horizontal axis, and the pressure p , in gigapascals (G Pa), on the
Which of the following systems of inequalities best describes the region where sillimanite can form?

Note:
We do not have the exact inequalities in the option, so we choose the one from the options which is the closest approximation of the inequalities that we have calculated. There are a couple of formulas and concepts used here, such as the equation of a line passing through two points and the concept that the region below a line is given by replacing the equality sign with less than or equal to in the standard form of the equation and vice versa.