A and B together can do a certain work in 36 days, whereas B and C together can do it in 30 days. A, B and C together can complete the same work in 24 days. In how many days can A alone complete \(33 \frac{1}{3} \)% of the same work?

An article was sold at a profit of 12%. If the cost price would be 10% less and selling price would be Rs.5.75 more, there would be profit of 30%. Then at what price it should be sold to make profit of 20%.

If sinθ + sin²θ + sin³θ = 1, then cos⁶θ - 4cos⁴θ + 8cos²θ is

A and B working alone can complete a work in 8 days and 12 days, respectively. They started working together, but A left 2 days before completion of the work. In how many days was the work completed?