Which of the following is true for 0° < θ < 90° ?

A can complete a certain work in 30 days. He started the work. After 4 days, B joined him and the whole work was completed in 10 days from the beginning. B alone can complete one-third of the same work in:

Varun and Syan can do a work in 3 days. Syan and Anil can do it in 4 days, and Anil and Varun can do it in 6 days. How many days will Anil alone take to do the work?

A sum of ₹5,000 is divided into two parts such that the simple interest on the first part for \(4\frac{1}{5} \)years at \(6\frac{2} {3}\% p.a \). is double the simple interest on the second part for \( 2\frac{3}{4} \)  years at 4% p.a. What is the difference between the two parts?