100 POINTS + BRAINLIST 1) Flying with the wind, a plane flew 600 miles in 3 hours. Flying against the wind, the plane could fly only 300 miles in the same amount of time. Find the speed of the plane in calm air and the speed of the wind.
2) Cakes are made to sell at a bakery. It takes 2 hours to make a mini-sized cake and 3 hours to make a full-size cake. The owner of the bakery will make a profit of $14 for each mini-sized cakes sold and $22 for each full-sized cakes sold. If the bakery owner has no more than 40 hours available to make the cakes and wants to have at least 16 cakes to sell, how many of each size cakes should be made to maximize profit?
3) Points A & B on a national highway are 120 miles apart from each other. One car starts from A and another car starts from B at the same time and they start going in the same direction indicated by AB, each at some individual constant speeds. The first car overtakes the second in 4 hours. However, had the second car moved in the opposite direction BA, then A & B would have met each other in 2 hours after their start. Find the speed of the car that started at Point A.
4) The sum of the digits of a two-digit number is 12. The number obtained by interchanging the two digits exceeds the initial number by 18. What is the initial number?
5) Two people can paint a house in 12 hours. Working individually one of the people can paint the house in 10 hours more than it takes the other person to paint the house. How long would it take each person working individually to paint the house?
6) If |x| + x + y =10 AND lyſ + x - y =12 then find the value of x + y
7) $510 is divided among A, B & C such that A gets 2/3 of what B gets and B gets 14 of what C gets. Find what amounts A, B & C get respectively.
8) Two numbers are in the ratio 1:2 If 7 is added to both, the ratio changes to 3:5 Find the greater number of the two.
9) Out of all the people eligible to vote, 8% are between ages 18 to 21 years. In an election, 75% of those who were eligible and between age 18 & 21 actually voted. What is their percentage out of all the people eligible to vote?
10) In a class, the number of boys is more than the number of girls by 12% of the total strength. Find the ratio of boys to girls.