Maths Resource

  For going to a city B from city A, there is a route via city C such that AC  perpendicular to CB, Ac = 2 x km and CB = 2(x + 7) km. It is proposed to  construct a 26 km highway which directly connects the two cities A and B. Find  how much distance will be saved in reaching city B from city A after the  construction of the highway

  A fire in a building B is reported on telephone to two fire stations P and Q, 20 km apart from each other on a straight road. P observes that the fire is at an angle of 60 ∘ to the road and Q observes that it is at an angle of 45 ∘ to the road. Which station should send its team and how much will this team have to travel?

Another important concept that is used in time work problems is the combined efficiency of two or more persons. In questions on time and work, the rates at which certain persons or machines work alone are usually given, and it is necessary to compute the rate at which they work together (or vice versa). Let us say, for example, it takes 3 & 6 hours for Bahubali and Kattappa, respectively, to break a dam working alone. So, in 1 hour Bahubali would have broken one-third or 1/3rd or 33% of the dam and Kattappa would have broken one-sixth or 1/6th or 16.67% of the dam. In 2 hours, Bahubali would have destroyed 1/3*2 or 33% *2 = 66.66% of the dam and kattappa would have destroyed 1/6th *2= 1/3= 33.33% of the dam. So if Both Bahubali and Kattappa work together, they would have destroyed 66.66+ 33.33 (2/3+1/3) or 100% of the dam in 2 hours. Therefore, if both worked together for 1 hour, they would have destroyed 1/3 + 1/6= ½ or half of the dam. Thus in 2 hours, the dam is destroyed. G...