For the following questions answer them individually
A man purchased 20 dozens of pencils at the rate of ā¹240 per dozen. Two-thirds of the pencils were sold at the rate of ā¹25 each and the rest of the pencils sold at ā¹22 each. What is the average percentage of profit?
If x and y are two positive integers such that the highest common divisor of these numbers is two, then how many values can x take if x + y = 99, simultaneously?
Ajay, Bharat and Chandu can complete a piece of work in 24 days, 30 days, and 32 days, respectively. Ajay and Chandu work on the first day and Bharat completes the same work the next day. If they work in this way, in how many days can they complete the work?
If $$\frac{1}{2+\frac{1}{3+\frac{1}{4+\frac{1}{\frac{1}{x}}}}}$$ =Ā $$\frac{68}{157}$$, then the value of $$x^{3} + 3x^{2} - 9x + 5$$.
100 people are standing in a row such that the distance between the person standing at the $$n^{th}$$ place and the person standing at the $$(n + 1)^{th}$$ place is exactly (n + 1) metres. What is the distance between the person standing at the $$1^{st}$$ place and the person standing at the $$50^{th}$$ place in the row (in metres)?
A merchant has 300 pumpkins. The merchant sells two-third of the pumpkins at the marked price, 75% of the remaining pumpkins at 20% reduced price, and finally the remaining pumpkins at 40% off the marked price. If the total sell price of pumpkins is Rs. 2750, then the original selling price of each pumpkin is
A die is thrown twice. What is the probability that at least one of the two dice shows the number 4?
Let $$f(x) = \sin x + \sin 2x + \cos 3x$$. Then the graph of $$g(x) = \sin (x + \pi) + \sin (2x + \pi) + \cos (3x + \pi)$$:
A roly-poly toy is made by joining a hemispherical bottom with a conical top. The diameter and the volume of the hemisphere are the same as the diameter of the base and volume of the cone, respectively. The toy is vertically cur at half of its height. If the diameter of the base sphere was 4 inch, what would the volume (in $$inch^{3}$$) of the upper half of the toy be?
One man and one woman can complete a piece of work in 18 days while four men and three women can complete the same work in 5 days. In how many days can two men and three women complete the same work?