Two circles with radii r₁ = 7 cm and r₂ = 3 cm have their centres 20 cm apart. Find the length of the transverse common tangent between them.

ABCD is a quadrilateral with ∠A = 3(x + 2)°, ∠B = 2(2x − 7)°, ∠C = 69° and ∠D = ∠C − 8°. What is the value of ∠B?

Pipe A can fill a tank in 12 hours, pipe B can fill the same tank in 21 hours and pipe C can fill the same tank in 16 hours. The time taken by them to fill the same tank if they operate together is:

A and B invest ₹50,000 and ₹70,000, respectively, in a business. After 1 year, the total profit is distributed, including simple interest a 10% per annum on the capital of each partner. If the total profit, including interest, is ₹18,000, what is A's share of the profit?

Given that 17^0.24 = x, 17^0.51= y and x^z = y⁴, then the value of z is close to:

The amount on a sum of ₹6,500 at 20% per annum compound interest, compounded annually, in 2 years will be:

By selling 6 tablets for a rupee, a man loses 35%. To gain 30% how many must he sell for a rupee?

A software developer sells a license for a new application to a reseller at a 20% discount. An installment and support fee of 15% is added to the discounted price. The reseller then sells the license for ₹7800 more, making a 25% profit. Determine the original marked price of the software license by the developer.

A 325 m long train overtakes a man moving at a speed of 5 km/hr (in the same direction) in 45 seconds. How much time (in seconds) will it take this train to completely cross another 440 m-long train, moving in the opposite direction at a speed of 20 km/hr?

In an election between two candidates, 95% of the registered voters cast their vote and 20% of the votes polled were found invalid. The winning candidate got 59% of the valid votes and won the election by a margin of 1881 votes. How many voters were registered?