(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

The weight of 50 workers is given below:

Draw an ogive of the given distribution using a graph sheet. Take 2 cm = 10 kg on one axis and 2 cm = 5 workers along the other axis. Use a graph to estimate the following:

1) The upper and lower quartiles.

2) If weighing 95 kg and above is considered overweight, find the number of workers who are overweight.

The marks obtained by 100 students in a Mathematics test are given below:

Draw an ogive for the given distribution on a graph sheet.

Use a scale of 2 cm = 10 units on both axes.

Use the ogive to estimate the:

1) Median.

2) Lower quartile.

3) A number of students who obtained more than 85% marks in the test.

4) A number of students who did not pass in the test if the pass percentage was 35.

What least number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional?

Using the properties of proportion, solve for x, given `(x^4 + 1)/(2x^2) = 17/8`.

6 is the mean proportion between two numbers x and y and 48 is the third proportional of x and y. Find the numbers.

If x, y, z are in continued proportion, prove that `(x + y)^2/(y + z)^2 = x/z`

The sides of a right-angled triangle containing the right angle are 4x cm and (2x – 1) cm. If the area of the triangle is 30 cm²; calculate the lengths of its sides.

The hypotenuse of a right-angled triangle is 26 cm and the sum of other two sides is 34 cm. Find the lengths of its sides.

The sides of a right-angled triangle are (x – 1) cm, 3x cm and (3x + 1) cm. Find:

1. the value of x,
2. the lengths of its sides,
3. its area.

The hypotenuse of a right-angled triangle exceeds one side by 1 cm and the other side by 18 cm; find the lengths of the sides of the triangle.

The diagonal of a rectangle is 60 m more than its shorter side and the larger side is 30 m more than the shorter side. Find the sides of the rectangle.

The perimeter of a rectangle is 104 m and its area is 640 m². Find its length and breadth.

A footpath of uniform width runs round the inside of a rectangular field 32 m long and 24 m wide. If the path occupies 208 m², find the width of the footpath.

Two squares have sides x cm and (x + 4) cm. The sum of their area is 656 sq. cm. Express this as an algebraic equation in x and solve the equation to find the sides of the squares.

The dimensions of a rectangular field are 50 m and 40 m. A flower bed is prepared inside this field leaving a gravel path of uniform width all around the flower bed. The total cost of laying the flower bed and gravelling the path at Rs. 30 and Rs. 20 per square metre, respectively, is Rs. 52,000. Find the width of the gravel path.

An area is paved with square tiles of a certain size and the number required is 128. If the tiles had been 2 cm smaller each way, 200 tiles would have been needed to pave the same area. Find the size of the larger tiles.

A farmer has 70 m of fencing, with which he encloses three sides of a rectangular sheep pen; the fourth side being a wall. If the area of the pen is 600 sq. m, find the length of its shorter side.

A square lawn is bounded on three sides by a path 4 m wide. If the area of the path is `7/8` that of the lawn, find the dimensions of the lawn.

The area of a big rectangular room is 300 m². If the length were decreased by 5 m and the breadth increased by 5 m; the area would be unaltered. Find the length of the room.

A car made a run of 390 km in ‘x’ hours. If the speed had been 4 km/hour more, it would have taken 2 hours less for the journey. Find ‘x’.