A man reaches a spot from his home in 6 hrs by walking, but he can reach the same spot from his home within 2 hrs by cycle. If the given average cycling speed is 7km/hr faster than his average walking speed, then find the average cycling and walking speeds.

Given a rectangular room whose width is 4/7 of its length y and perimeter z. Write down an equation connecting y and z. Calculate the length of the rectangular room when the given perimeter is 4400 cm.

A drainage tile is a cylindrical shell 21 cm long. The inside and outside diameters are 4.5 cm and 5.1 cm respectively. What is the volume of the clay required for the tile?

Find the area of the given figure.

Four years back in time, a father was 3 times as old as his son then was. 8 years later father will be 2 times as old as his son will then be. Find the ages of son and father.

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 $20 less or equal than s less or equal than 75$ .
$M left parenthesis s right parenthesis equals negative 1 over 24 s squared plus 4 s minus 50$
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 $M to the power of straight prime left parenthesis S right parenthesis greater than 0$ ., on the left side
and the function is decreasing, i. e $M to the power of straight prime left parenthesis s right parenthesis less than 0$ ., on the right hand side, then we say that is a local maxima.

The gas mileage M (s), in miles per gallon, of a car traveling s miles per hour is modeled by the function below, where $20 less or equal than s less or equal than 75$ .
$M left parenthesis s right parenthesis equals negative 1 over 24 s squared plus 4 s minus 50$
According to the model, at what speed, in miles per hour, does the car obtain its greatest gas mileage?

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, $text if end text MP equals 9 cm comma MD equals 7 cm comma MC equals 6$ cm, $MB equals 4 cm text and end text MA equals 2 cm$

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. $GE equals 14 cm comma HF equals 10 cm comma AD equals 24 cm straight & BC equals 12$
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