Inside a rectangular park of dimensions 100m × 80m, walking paths 3m wide are to be constructed as shown in the figure given below (a 3 m path along the inside of the boundary, plus one path parallel to the length and one parallel to the width crossing in the middle). Find the cost of construction of paths at the rate of ₹120/m². [Figure: see page 37 of source PDF]

The length of a hall is 22 m and the width is 18 m. If the sum of the areas of the floor and the roof is equal to the total area of the four walls, then what is the volume of the hall?

The co-ordinates of midpoints of the sides AB, BC, and CA of a triangle ABC are (3, 6), (5, 3), and (8, 5) respectively. The co-ordinates of vertex A are:

Four years ago, the ages of Rekha and her mother were in the ratio 1:6. Five years hence, the ratio will become 1:3. How old will the mother be after 10 years from now?

If a + b + c = −10 and ab + bc + ac = 10, then the value of the expression a³ + b³ + c³ − 3abc is:

Two pipes 'A' and 'B' can fill a water tank in 30 minutes and 20 minutes, respectively. Initially pipe 'A' was opened and after 5 minutes, pipe 'B' was also opened. Find the total time (in minutes) taken by the pipes to fill the tank.

Three numbers are in the ratio 4:5:7 and their LCM is 5040. Their HCF is:

Two trains 'A' and 'B' started running at the same time. Train 'A' takes 3 hours more than train 'B' to cover 540 km. But if train 'A' doubles its speed, it covers 540 km in 1½ hours less than train 'B'. What is the speed (in km/h) of train 'B'?

From the passage: Study the pie charts and answer the following questions: In a manufact...

By what percentage are the number of female employees of levels 'A' and 'B' taken together is greater than the number of male employees of levels 'A' and 'B' taken together? [Figure: see page 41 of source PDF]