One Click Prep | Sujoy Kumar Datta

Let us take a question on mixtures. We will try to solve it using five different methods A 80 liter solution contains 20% alcohol by volume. A part of the solution is removed and replaced with pure alcohol to bring the alcohol concentration to 25%. What is the volume of the solution that was removed? Method 1 - Using basic percentage computations and setting up an equation Volume of alcohol in the 80 liters solution = 20% of 80 = 20 × 80 ÷ 100 = 16 liters Let volume of solution removed = v liters This will also have 20% alcohol ⇒ Volume of alcohol removed = 20 × v ÷ 100 = 0.2v liters Volume of alcohol added = v liters (Note: replace imples adding a quantity equal to what was removed) Thus, total alcohol volume = (16 - 0.2v + v) = (16 + 0.8v) liters Total solution volume = 80 liters Thus, required percent = [(16 + 0.8v) ÷ 80] × 100 Thus, we have: [(16 + 0.8v) ÷ 80] × 100 = 25 ⇒ 16 + 0.8v = 20 ⇒ v = 5 liters - Answer Method 2 - Using the fact that the concentration of alcohol remains u...

How to solve Removal and replacement questions We often get questions involving  removal and replacement of mixtures where a part of a mixture is removed and replaced by some other solution. Say, a vessel contains different constituents in some given ratio. A fraction of the solution is removed and some quantity of some constituent is added to the solution. This process is repeated multiple times and the final ratio of constituents in the mixture has to be determined. Though this looks very complicated, we can solve it simply, in fact, in a single line! We just need to understand the fact that if a fraction,  f  of the solution is removed, the same fraction of each constituent also gets removed, and hence, the fraction  (1-f)  of each constituent is left, and as a result, after removal, the ratio of the constituents remains unchanged. This is very easy to understand. Say, you have a sugar solution in a glass and you drink a part of it. The remaining part would t...

Percentage & Percentage change Percent (read as per cent) means ‘every hundred’, or, essentially, ‘out of 100’. If we are given a fraction, we can simply convert it to a percentage by multiplying 100. Say, we have ½, which, when multiplied with 100 becomes ½ x 100 = 50%. What do we mean by a percentage change? Say, a person has 20 chocolates. If his number of chocolates is increased by 10%, what does it mean? First of all, let us see what is doesn’t mean: after the increase, the number of chocolates with him is  NOT  20 + 10 = 30, nor is it 20 +  10 / 100  = 20.1 When we talk of a percent increase, we must understand on what  BASE VALUE  is the percentage change working on. In this case, obviously, the 10% increase is 10% of the number of chocolates he has, i.e. 20. Thus, the number of chocolates with him would become: 20 + 10% of 20 = 20 + 20 x  10 / 100  = 22 Observe that:  20 + 20 x  10 / 100  = 20 x (1 +  10 / 100 ) = 2...

CAT 2025 – a 9 month journey Expected format of CAT 2025 How to prepare for CAT 2025 With another 9 months left for CAT 2025 (expected to be held towards the end of November), how should you start your preparation? We know that the CAT tests skills in three areas – Quantitative Aptitude, Logical reasoning & Data Interpretation, and Verbal Ability. Thus, to excel in this test, you need to devote time equally to each of the three areas. How to effectively do that is what we will discuss. Take stock of the situation Those who have already started preparing for CAT 2025 sometime back, would be aware of exactly what sort of skills are required to excel in these three areas. They would also be aware about which area they are particularly weak in. Needless to say, you need to devote the major part of your preparation to overcome your weaknesses. However, those who have decided to start just now for CAT 2025, don’t worry! You are not late in starting your preparations. But, first you need ...