X, Y and Z can do a piece of work in 46 days, 92 days and 23 days, respectively. X started the work. Y joined him after 2 days. If Z joined them after 8 days from the beginning, then for how many days did X work? 

A vertical pole and a vertical tower are on the same level of ground in such a way that from the top of the pole, the angle of elevation of the top of the tower is 60⁰ and the angle of depression of the bottom of the tower is 30⁰. If the height of the tower is 76 m. then find the height (in ₹) of the pole.

In a ∆ ABC, points P, Q and R are taken on AB, BC and CA, respectively, such that BQ=PQ and QC=QR. If ∠BAC = 75⁰, what is the measure of ∠PQR (in degress)?

The value of   $${sin23^0cos67^0+sec52^0sin38^0+cos23^0sin67^0+cosec52^0cos38^0}\over cosec^220^0-tan^270^0$$ is

A can finish a piece of the work in 16 days and B can finish it in 12 days. They worked together for 4 days and then A left. B finished the remaining work. For how many total number of days did B work to finish the work completely?

The average weight of P and his three friends is 55 kg. If P is 4 kg more than the average weight of his three friends, what is P's weight (in kg)?

If (x + 6y) = 8, and xy = 2, where x > O, what is the value of (x³+216y³)?

Some students (only boys and girls) from different schools1 appeared for an Olympiad exam. 20% of the boys and 15% of the girls failed the exam. The number of boys who passed the exam was 70 more than that of the girls who passed the exam'. A total of 90 students failed. Find the number of students that appeared for the exam.