Topic Details (Notes format)

How to Solve Direct and Inverse Variation Problems

Subject: Mathematics

Book: Maths Mastery

Direct variation follows y = kx, where y changes proportionally with x (e.g., doubling x doubles y). Inverse variation follows y = k/x, implying that multiplying x by a factor divides y by the same factor. For instance, if y ∝ x, you might have y = 3x; doubling x from 2 to 4 changes y from 6 to 12. Conversely, if y ∝ 1/x, and x changes from 2 to 4, y becomes half. Variation problems are integral in physics (Ohm’s Law), chemistry (pressure-volume relationships), and everyday concepts like speed-time relationships. Mastering them helps you interpret how one quantity shifts in response to another.

Practice Questions

A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?

View Question

What is the square root of 121?

View Question

If sin(A) = 1/2 and A is acute, what is the value of A?

View Question

A cone has a base radius of 7 cm and height of 24 cm. What is its volume?

View Question

What is the probability of drawing a king from a standard deck of 52 playing cards?

View Question

A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

View Question

If the cost price of an item is Rs. 400 and the selling price is Rs. 500, what is the profit percentage?

View Question

If a right triangle has legs of 9 cm and 12 cm, what is the length of the hypotenuse?

View Question

A square is inscribed in a circle with a radius of 5 cm. What is the area of the square?

View Question

If x + 1/x = 5, what is the value of x^2 + 1/x^2?

View Question