Quantitative Aptitude - Arithmetic Ability Questions

The vertical angle A of an isosceles triangle ΔABC is three times the angle B of it. The measure of the angle A is

What is the simplified value of (cos A + sin A)(cot A + tan A)?

The ratio of cost price and selling price 25:26. The percent of profit will be

There are two numbers such that the first number is half of the second number. If their average is 57, then what is the first number?

Working together, pipes A and B can fill an empty tank in 10 hours. They worked together for 4 hours and then B stopped and A continued filling the tank till it was full. It took a total of 13 hours to fill the tank. How long would it take A to fill the empty tank alone?

P does half as much work as Q in 1/3 of the time. If together they take 15 days to complete a work, how many days will P take to do it alone?

Incentre of Δ ABC is I. ∠ABC = 90° and ∠ACB = 70°. ∠AIC is

∆DEF is right angled at E. If m∠F = 45°, then find the value of (cosecD - 1/√3).