Simplify $$ ({Sinθ\over{1+cosθ}}+{1+cosθ\over sinθ})({1\over (tanθ+cotθ)})$$

A sum of ₹4000 is lent out in two parts, one at 8% simple interest and the other at 10% simple interest. If the annual interest is ₹352. The sum lent at 8% is

The probabilities of solving a problem by three students A, B and C are  $$3\over 7$$, $$5\over 9$$ and $$1\over 5$$ respectively. The probability that problem will be solved is:

A, B and C together invests ₹53,000 in a business. A invests ₹5,000 more than B and B ₹invests 6,000 more than C. Out of a total profit of ₹31,800, find the share of A.

A can do a piece of work in 24 day, B in 32 days and C in 64 days. All begin to do it together, but A leaves after 6 days and B leaves 6 days before the completion of the work. How many days did the work last?

A is as efficient as B and C together. Working together A and B can complete a work in 36 days and C alone can complete it in 60 days. A and C work together for 10 days. B alone will complete the remaining work in:

A jeep travels to a place 300 km away at an average speed of 60 km/h and returns at a speed of 30 km/h. What is the average speed (in km/h) for the whole journey?

Rahul invested equal sums of money at compound interest under two schemes A and B. Under scheme A, the interest rate was 10% per annum and under scheme B, the interest rate was 12% p.a. The compound interest after two years on the sum invested in scheme A was ₹1,050. How much is the interest earned under scheme B after two years, if the interest is compounded annually in both schemes?