Alligation in Time and distance

Problem 3

A man travels part of his journey by bicycle at 20 Km/h and remaining distance by car at speed of 70 Km/h covering the entire journey at an average speed of 50 Km/h. What is the ratio of distance covered by bicycle and car?

Solution –

Solving this problem by alligation is a matter of just a few seconds, here’s how.

As you can see in the picture, weighted average speed is 50 km/h so we keep it in the middle. Average speed of bicycle and car is taken as in visual components. We take average speed of bicycle on the left side and average speed of car on the right side (rule of thumb). By solving this simple alligation we find that ratio of time the man takes to complete the journey by bicycle and car is 2:3. But here we need to find the ratio of distance covered, so 2*20= 40 and for car 3*70=210

Ratio comes out to be 4:21.

Problem 4 – This is from the practice section from PERCENTAGE notes given in website..pls help to solve either in alligation method or any

A water tank contains 5% salt by weight. x litres of fresh water is added to 40 litres of tank water, so that the solution contains 2% salt. The value of x is

a) 40 b) 50 c) 55 d) 60

Solution –

Percentage of water in current mixture = (100 – 5) = 95%
Percentage of water in output mixture = (100 – 2 ) = 98%

Ratio of mixture and fresh water is 2:3. If there was 40 litres of mixture already available in the tank, we need add 40 × 3/2 = 60 litres

So the answer is D