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

A piece of cloth costs Rs. 300. If the piece was 5 metres longer and each metre of cloth costs Rs. 2 less, the cost of the piece would have remained unchanged. How long is the original piece of cloth and what is the rate per metre?

The hotel bill for a number of people for an overnight stay is Rs. 4800. If there were 4 more, the bill each person had to pay would have reduced by Rs. 200. Find the number of people staying overnight. 

A person was given Rs. 3000 for a tour. If he extends his tour programme by 5 days, he must cut down his daily expenses by Rs. 20. Find the number of days of his tour programme.

Ritu bought a saree for Rs. 60x and sold it for Rs. (500 + 4x) at a loss of x%. Find the cost price.

Paul is x years old and his father’s age is twice the square of Paul’s age. Ten years hence, the father’s age will be four times Paul’s age. Find their present ages.

The age of a man is twice the square of the age of his son. Eight years hence, the age of the man will be 4 years more than three times the age of his son. Find the present age.

Two years ago, a man’s age was three times the square of his daughter’s age. Three years hence, his age will be four times his daughter’s age. Find their present ages.

The length (in cm) of the hypotenuse of a right-angled triangle exceeds the length of one side by 2 cm and exceeds twice the length of another side by 1 cm. Find the length of each side. Also, find the perimeter and the area of the triangle.

If twice the area of a smaller square is subtracted from the area of a larger square, the result is 14 cm². However, if twice the area of the larger square is added to three times the area of the smaller square, the result is 203 cm². Determine the sides of the two squares.

Solve the following equation by factorisation :

x2 + 6x – 16 = 0

Solve the following equation by factorisation :

3x² + 11x + 10 = 0

Solve the following equation by factorisation :

2x² + ax – a²= 0

Solve the following equation by factorisation :

`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0

Solve the following equation by factorisation :

x(x + 1) + (x + 2)(x + 3) = 42

Solve the following equation by factorisation :

`(6)/x - (2)/(x - 1) = (1)/(x - 2)`

Solve the following equation by factorisation :

`sqrt(x + 15) = x + 3`

Solve the following equation by factorisation :

`sqrt(3x^2 - 2x - 1) = 2x - 2`

Divide 16 into two parts such that the twice the square of the larger part exceeds the square of the smaller part by 164.

Two natural numbers are in the ratio 3 : 4. Find the numbers if the difference between their squares is 175.

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