If $$ {x+{1\over {x}}=1}$$, then find the value of $$ {x^{208}+{x^{205}+x^{204}+x^{201}}}$$.

Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hour and 40 km/hour respectively. By the time they met the first train had travelled 100 km more than the second. Find the distance between P and Q?

The ratio of the present ages of Sunita and Vinita is 4 : 5. Six years hence the ratio of their ages will be 14 : 17. What will be the ratio of their ages 12 years hence?

A man has 60 pens. He sells some of these at a profit of 12 % and the rest at 8 % loss. On the whole, he gets a profit 11 %. How many pens were sold at 12 % profit.

A person invests money in three different schemes for 6 years, 10 years and 12 years at 10%, 12% and 15% simple interest respectively. At the completion of each scheme, he gets the same interest. The ratio of his investments is-

A sum of Rs.13,000 is to be paid back in 2 equal annual instalments. How much is each instalment if the interest is compounded annually at 8 % per annum?

The annual payment of Rs.1000 in  5 years at 4% per annum simple interest will discharge a debt of

ΔABC is an equilateral triangle in which D, E and F are the points on sides BC, AC and AB, respectively, such that AD ⊥ BC, BE ⊥ AC and CF ⊥ AB. Which of the following is true?