Two ship are on the opposite of a light house such that all three of them are collinear. The angels of depression of the two ships from the top of the light house are 30⁰ and 60⁰. If the ships are $$230 \sqrt { 3} \ $$ m apart, then find the height of the light house (in m).

The ratio of investment of Ram and Shyam is 11: 12 and the ratio of their profits is 2: 3. If Ram invested the money for 8 months, find for how much time Shyam invested his money?

If p³ – q³ = (p-q)[(p-q)²+xpq)] then the value of x is

Answer the following questions

P, Q and R alone can complete a piece of work in 24, 36 and 18 days respectively. P started working, after 2 days R joins with them and Q joins with them after another 2 days, then find the no of days P, Q and R worked together.

A woman buys a watch for Rs. 4,000 and sells it at a loss of 13%. What is the selling price of the watch?

G is the centroid of a triangle ABC, and the median is AD, the ratio of AD and GA is

Triangle PQR is such that PQ=9 cm, QR=6 cm, PR=7.5 cm and triangle PQR is similar to triangle XYZ. If XY=18 cm, find the value of YZ.

The graphs of the equations 3x-20y-2=0 and 11x-5y+61=0 intersect at P(a,b). What is the value of (a² + b² — ab)/(a² — b² + ab)?