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

A two digit number is such that the product of its digit is 14. When 45 is added to the number, then the digit interchange their places. Find the number.

Solve the following equation and give your answer up to two decimal places:
x² − 5x − 10 = 0

Solve the equation 2x `-(1)/x` = 7. Write your answer correct to two decimal places.

Solve the equation 3x² – x – 7 = 0 and give your answer correct to two decimal places.

A two digit number is such that the product of the digits is 12. When 36 is added to this number the digits interchange their places. Determine the number.

The side (in cm) of a triangle containing the right angle are 5x and 3x – 1. If the area of the triangle is 60 cm². Find the sides of the triangle.

By increasing the speed of a car by 10 km/hr, the time of journey for a distance of 72 km. is reduced by 36 minutes. Find the original speed of the car.

A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/hr more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car.

The speed of an express train is x km/hr arid the speed of an ordinary train is 12 km/hr less than that of the express train. If the ordinary train takes one hour longer than the express train to cover a distance of 240 km, find the speed of the express train.

Some students planned a picnic. The budget for the food was Rs. 480. As eight of them failed to join the party, the cost of the food for each member increased by Rs. 10. Find how many students went for the picnic.

Two pipes flowing together can fill a cistern in 6 minutes. If one pipe takes 5 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.

One fourth of a herd of camels was seen in the forest. Twice the square root of the herd had gone to mountains and the remaining 15 camels were seen on the bank of a river. Find the total number of camels.

An aeroplane travelled a distance of 400 km at an average speed of x km/hr. On the return journey the speed was increased by 40 km/hr. Write down the expression for the time taken for
The outward journey

An aeroplane travelled a distance of 400 km at an average speed of x km/hr. On the return journey the speed was increased by 40 km/hr. Write down the expression for the time taken for
the return Journey. If the return journey took 30 minutes less than the onward journey write down an equation in x and find its value.

Car A travels x km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
Write down the number of litres of petrol used by car A and car B in covering a distance of 400 km.

Car A travels x km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
If car A use 4 litre of petrol more than car B in covering the 400 km, write down and equation in x and solve it to determine the number of litre of petrol used by car B for the journey.

A shopkeeper purchases a certain number of books for Rs. 960. If the cost per book was Rs. 8 less, the number of books that could be purchased for Rs. 960 would be 4 more. Write an equation, taking the original cost of each book to be Rs. x, and Solve it to find the original cost of the books.

Two pipes running together can 1 fill a cistern in 11 1/9 minutes. If one pipe takes 5 minutes more than the other to fill the cistern find the time when each pipe would fill the cistern.

Solve the following quadratic equation by factorisation:
(x - 4) (x + 2) = 0

Solve the following quadratic equation by factorisation:
(2x + 3) (3x - 7) = 0