*The subject mathematics in CLAT may well be a nightmare for most students attempting the CLAT UG even though they may be from Science backgrounds. Some acknowledge that it is all Greek to them while others live in denial.*

**Ace Mathematics in CLAT**

CLAT is a filtering exam, not a selection exam! In order to clear CLAT UG in the 1^{st} attempt, it is enough if one correctly attempts all the non-difficult questions i.e. around 80-85% or 120-130 out of 150 marks. And to achieve that, mathematics plays an indispensable role because it carries 20 marks out of the total 150 marks i.e., nearly 13.33%.

The main catch here is that the weightage it represents is not limited to its face value of 13.33% because, given the certainty/objectivity of answers in the Math section and the lesser time taken to answer the questions (when compared to the other four subjects with paragraph questions), this 13.33% has a total value of around 20-25% if approached in the right manner as mentioned below.

By following the below mentioned detailed strategy, anybody can ace the Math section in CLAT. And it is a humble request to the students not to skip this section, because everybody can do the other four sections in CLAT and Math will be the only section which will be the deciding factor between the successful and the unsuccessful ones.

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**Introduction**

The subject mathematics may well be a nightmare for most students attempting the CLAT UG even though they may be from Science backgrounds. Some acknowledge that it is all Greek to them while others live in denial.

Consequently, in order to know one’s performance, it becomes imperative to take some form of an evaluation/exam. And ideally, I would suggest students try and attempt the math section from the previous year papers and aim for 15-18 correct answers in 15 minutes.

If a student scores anything below 15 in 15 minutes, then there are three possibilities/three categories of students which arise as mentioned below. Further, students who can score 15 marks or above in 15 minutes are all set to ace the CLAT exam and such students should focus on **maintaining their speed and accuracy** by practicing from various sources especially the previous year CLAT papers.

**First Category**

The first possibility is actually a happy problem i.e. when the student can solve all the questions correctly but **lags behind in time**. Such a performance by a student demonstrates that he/she has a strong foundation of basics and **only needs practice** and there is a ton of material on the internet for practice.

And practice here refers to the time-bound practice, i.e., setting a timer of 15 minutes to solve 20 questions correctly. As and when one achieves this target, one should avoid being complacent and continue practicing by reducing the target time to 10 minutes. After achieving this target, a student should try to maintain this level of speed and consistency by regular practice.

**Second Category / General Strategy**

In the second possibility, generally, the student is unable to solve the majority of the problems and this is a clear indicator of a **lack of foundation of basics**. Such a student should **revisit all the concepts and understand them from scratch**. Forgetting everything and beginning from the scratch is the only way forward for such students. Anything else will be equivalent to shooting arrows in the dark and hoping to strike bulls-eye. Students who are in this category should not lose hope because with a little bit of understanding and practice, they too can score at least 12-15 marks in the final CLAT exam. Persistence is the key to their problems.

Ideally, by dedicating 2-4 hours a day, it should take 1-2 weeks for such students to fully understand the basics. Once the students become familiar with the basics, they should put their newly acquired knowledge to test by solving problems on each of the chapters.

**Third Category**

In the third possibility, the student is able to solve around 12-15 problems in the time limit of 15 minutes but is **not able to solve the rest of the problems correctly**. This is a clear indicator of a **lack of a complete foundation of basics**. Such a student should **revisit the unknown/partially known concepts and understand them from scratch**. Forgetting any prior knowledge of such unknown/partially known concepts and beginning from the scratch is the only way forward for such students. Anything else will be equivalent to shooting arrows in the dark and hoping to strike bulls-eye.

Students who are in this category have to compulsorily understand the basics of any unknown or partially known concepts to increase their scores. Otherwise, even if they practice only math alone, they may still end up with 12-15 marks in the final exam.

Also, it is necessary to understand the basics of all the chapters of 10^{th} standard maths because CLAT UG has no obligation to follow their previous year patterns and they (CLAT consortium) may ask more questions from any given topic/chapter(s).

Further, it is generally observed that some students, who belong to such a category, tend to remember the answers but this is not a healthy practice because, in the final exam, there is no guarantee that questions will come from any single material/source. The only thing which one can be sure of is that all the questions in CLAT 2020 will be on the lines of 10^{th} standard math and nothing above that.

**Syllabus for Clat UG in Mathematics**

Serial no. | Chapter | Details |

1. | Mensuration | Area and Volume |

2. | Commercial Mathematics | Interest, Profit, Loss and Discounts, Percentage, Partnership |

3. | Modern Mathematics | Permutation and Combination, Probability, Clocks and Calendars |

4. | Data Interpretation | Graphs and Charts |

5. | Arithmetic | Number System, LCM, HCF, Logarithm & Functions, Ratio & Proportions, Time & Work |

**General Do’s and Don’ts**

**Dos:**

- Understand the basics before practising.
- Once you are thorough with the basics then practice as much as you can.
- After reaching the target time and score of 15 under 15, continue practising to maintain the speed and accuracy.
- Attempt all the 80-85% of non-difficult questions and then go for the difficult questions.
- Always attempt math without fear and without stress, ideally in the last 30 minutes.
- Always have a buffer time of 10-15 minutes to recheck the entire paper including the math section.
- Solve questions from different sources and on all the topics.
- Some questions need not be solved till the end. Look at the options and see if any options can be eliminated by substitution in the problem/equation.
- Order of reading for solving questions: Options > Individual Question > Paragraph question (if applicable).
- Some tough questions can be solved easily from the options by elimination or option substitution method. If you could eliminate only 2 out of 4 options, then try substituting the options in the question/equation.
- Always carry a pen, pencil, eraser, sharpener and paper to the exam hall if it is allowed.

**Don’ts:**

- Don’t skip the Math section or any chapter thereof because there is no guarantee that CLAT will have equal weightage for all chapters/topics even if there is a pattern in the previous year papers.
- Don’t try to remember the answers.
- Don’t keep solving blindly without knowing the basics.
- Don’t beat yourself up because somebody else is better at Math because in 99.9% of the cases, they have spent more time on mastering it than you.
- Don’t get complacent after achieving the target time and score, because the D-day might not be your day and the only thing that will help you will be your consistent practice.
- Don’t get stuck on one single question because chances are it may be actually wrong and will get cancelled after the key is released. So don’t waste time on one single question. Just keep moving.
- Don’t cheat in the exam. It is not and it will never be worth the risk!
- Don’t mark answers based on pure guesswork because the probability of your answer being wrong is ¾ or 75% of the times your guess will be wrong.

**Examples**

**Q1 –** The distance between Delhi and Agra is 200 km. The New Delhi Shatabdi Express starts from Delhi towards Agra at 12 noon. On the way, it crosses a bridge measuring 200 m in 35 seconds, and a pillar on the bridge in 25 seconds. At the same time, the Hazrat Nizamuddin Singrauli SF Express, which is 300 m in length, starts from Agra towards Delhi at 58 km/h. However, due to the holiday season, the railways decided to run the holiday special train Sheetkal Express, which is 400 m in length, from Delhi to Agra, leaving at 12:15 pm at a speed of 84 km/h.

**1.1 At what distance from Agra will the New Delhi Shatabdi Express and the Hazrat Nizamuddin Singrauli SF Express cross each other?**

- 100.16 km
- 72,729 m
- 89.32 km
- 82.91 km

The correct answer is (c)

**Explanation – **

Length of the bridge = 200 m

Let the length of the New Delhi Shatabdi Express be ‘L’ and its speed be ‘S’.

L + 200 = 35 x S

S = (L + 200) / 35

L = 25 x S

S = L / 25

L / 25 = (L+200) / 35

35L = 25L + 5000

10L = 5000

L = 500 m

Therefore, speed S = 500 / 25 = 20 m/s

(20m/s x 18) / 5 = 72 km/h

Distance between the 2 cities = 200 km

Speed of New Delhi Shatabdi Express = 72 km/h

Speed of Hazrat Nizamuddin Singrauli SF Express = 58 km/h

Since the trains are moving towards each other the speed of the trains will be added up to compute the time taken for the trains to cross each other.

Therefore, Total Speed = 72 + 58 = 130 km/h

Distance = Speed x time

200 = 130 x time

The time it will take for the two trains to meet = 200/130 = 1.54 hours

Therefore, the trains will meet 1.54 hours after starting from their respective locations.

Distance from Agra = 1.54 hours x speed of Hazrat Nizamuddin Singrauli SF Express (Starts from Agra)

= 1.54 x 58 = 89.32 km

Distance from Delhi = 1.4 x New Delhi Shatabdi Express = 1.54 x 72 = 110.88 km

**1.2 Assuming no stoppages, at what time will the Sheetkal Express overtake the New Delhi Shatabdi Express?**

- 1:00 pm
- 1:30 pm
- 1:15 pm
- 1:45 pm

The correct answer is (d)

**Explanation**

Speed of New Delhi Shatabdi Express = 72 km/h. (See Rationale for 1.1)

Speed of Sheetkal Express = 84 km/h.

Time at which New Delhi Shatabdi Express starts = 12 pm

Time at which Sheetkal Express starts = 12.15 pm

Therefore, let us assume that the time taken by Sheetkal Express to overtake New Delhi Shatabdi Express is t.

Both the trains would have covered the same distance D at the time of overtaking.

D = 72 x (t + 0.25) [As New Delhi Shatabdi Express started 15 minutes early)

D = 84 x t

72 x (t + 0.25) = 84 x t

72t + 18 = 84t

84t – 72t = 18

t = 18 / 12

t = 1.5 hours.

Therefore, the Sheetkal Express would overtake the New Delhi Shatabdi Express at 1.45 pm.

**1.3 How much time will the New Delhi Shatabdi Express and the Hazrat Nizamuddin Singrauli SF Express take to cross each other and how much time will the New Delhi Shatabdi Express and the Sheetkal Express take to cross each other?**

- 22.15 seconds, 4.5 minutes
- 0.5 minutes, 300 seconds
- 270 seconds, 330 seconds
- 1.8 minutes, 37 seconds

The Correct Answer is (a)

**Explanation**

Since the New Delhi Shatabdi Express and the Hazrat Nizamuddin Singrauli SF Express cross each other in opposite directions, the speeds of the trains and the distance must be added.

Therefore, the formula Distance = Speed x Time is modified as,

(Length of Train 1 + Length of Train 2) = (Speed of train 1 + Speed of train 2) x Time

Length of New Delhi Shatabdi Express is 500 m (See Rationale for 1.1)

Speed of Hazrat Nizamuddin Singrauli SF Express = 58 km/h

(58 km/h x 5) / 18 = 16.11 m/s

(500 metres + 300 metres) = (20 m/s + 16.11 m/s) x Time

800 metres = 36.11 m/s x Time

Time = 22.15 seconds

Since the New Delhi Shatabdi Express and the Sheetkal Express are travelling in the same direction, the distance is the added length of both the trains, but we subtract the speed of the trains.

500 metres + 400 metres = 900 m = .9 km

0.9 km = 84 km/h – 72 km/h

t =0.9/12 = (9/120) x 60 = 4.5 minutes

**Conclusion**

Following the above-mentioned strategies should ideally help any person to ace the Math section irrespective of their current state of preparation. Also, another thing to keep in mind for mastering Math is that questions in this section require a stress-free mind. So, the ideal time to attempt the math section would be in the last 30 minutes (15 minutes for Math section and 10 minutes for revising the paper).

Further, it is necessary to identify which question to leave and which question to attempt since there will be some questions (ideally 2-3 questions) which cannot be completed in the targeted time of 15 minutes and will require 2-4 minutes for each question. Such difficult questions should be attempted at the last and can be left due to time paucity because scoring all the non-difficult questions should do. Doing all the non-difficult questions in the math section would ideally result in a score of around 80% of the marks i.e. 16 out of 20 in fewer than 15 minutes.

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