Mathematical Sk...

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:

Farhan and Kunal invested some money to start a company and the share of Farhan in the investment is$35\%$ while the share of Kunal is $65\%$. After one year, Farhan and Kunal increased their investment by$20\%$ and$30\%$ respectively. At the end of the second year, the revenue of the company is Rs.$12,650$ and there is neither any profit nor loss. Find the amount invested by Farhan initially?

If the simple interest for 4 years is Rs. 2000 at 10% rate of interest. Find the compound interest for the 2 year on same rate.

If \(\sin ^{-1} \frac{2 a}{1+{a}^{2}}+\sin ^{-1} \frac{2 {b}}{1+{b}^{2}}=2 \tan ^{-1} {n}\) then?

Ajit, Anand, and Ayush enter into a partnership investing their Money in the ratio \(3:4:5\). What is the ratio of their time period of investments if Ayush receives Rs \(15000\) as a share from a profit of Rs \(51000\)? Given that Ajit invested twice the time Ayush invested.

A bag contains 17 tickets numbered from 1 to 17. A ticket is drawn at random, then another ticket is drawn without replacing the first one. The probability that both the tickets may show even numbers by:

The ratio between the speed of the boat in still water to the speed of the stream is 5: 2. If 224 km is traveled by downstream in 4 hours then find the difference between the speed of the boat in still water and the speed of the stream?

The efficiency of Varun is \(\frac{1}{5}\) more of Karan. If both together can do a work in 30 days. In how much time Karan alone can do it?

A person sells an article at a profit of 10%. Had he bought it at Rs.___ less and sold for Rs.___ more, then he would have gained 25%. The cost price of the article is Rs. 120. Which of the following options satisfies the two blanks in the question?

A. 12, 5

B. 20, 10

C. 12, 3

D. 15, 10

Rakesh completes a math project in 10 days, while Ravi takes 15 days. Rakesh starts a project and works for 4 days alone, after 4 days Ravi joins and they work together for 2 days. Then a third person Anas joins and they three work together for \(\frac{16}{13}\) days and complete the project. In how many days can Anas complete a project alone?