CLAT Maths Questions with Solutions 2025 - Quantitative Techniques Questions

Passage 1
Read the passage below and answer the following question.
Cheating is considered a criminal offence under the Indian Penal Code. It is done to gain profit or advantage from another person by using some deceitful means. The person who deceives another knows for the fact that it would place the other person in an unfair situation. Cheating as an offence can be made punishable under Section  of the . Scope of Section  Cheating is defined under Section  of the Indian Penal Code as whoever fraudulently or dishonestly deceives a person to induce that person to deliver a property to any person or to consent to retain any property. If a person intentionally induces a person to do or omit to do any act which he would not have done if he was not deceived to do so and the act has caused harm to that person in body, mind, reputation, or property, then the person who fraudulently, dishonestly or intentionally induced the other person is said to cheat. Any dishonest concealment of facts that can deceive a person to do an act that he would not have done otherwise is also cheating within the meaning of this section. Essential Ingredients of Cheating requires · deception of any person. Fraudulently or dishonestly inducing that person to deliver any property to any person or to consent that any person shall retain any property; or · intentionally inducing a person to do or omit to do anything which he would not do or omit if he were not so deceived, and the act or omission causes or is likely to cause damage or harm to that person in body, mind, reputation or property.
Deceit– a tort arising from an untrue or false statement of facts which are made by a person, recklessly or knowingly, with an intention that it shall be acted upon by the other person, who would suffer damages as a result. 
Fraud – a false or untrue representation of the fact, that is made with the knowledge of its falsity or without the belief in its truth or a reckless statement that may or may not be true, with an intention to induce a person or individual to act independent of it with the result that the person acts on it and suffers damages and harm. In other words, it is a wrong act or criminal deception with an intention to result in financial or personal gain.
Question - 1 
 went to a moneylender, , for the loan.  intentionally pledges the gold article with  taking the loan.  knows that the article is not made of gold. After a few days,  leaves the village. Decide.

Read the passage carefully and answer the question

The Contract should be performed by the promisor himself. However, in certain cases, it can also be performed by his agents or legal representatives. It all depends upon the intention of the parties. Normally a contract can be performed by the following persons. 

1. Promisor himself: If from the nature of the contract it appears that it was the intention of the parties that the promise should be performed by the promisor himself, such promise must be performed by the promisor. This usually applies to contracts involving personal skill, task, or artwork. 
2. Promisor or his Agent: Where the contract does not involve the personal skill of the promisor, the contract could be performed by the promisor himself or by any competent person employed by him for the purpose, 
3. Legal Representatives: The contracts which do not involve any personal skill or taste, may be performed by his legal representative after the death of the promisor.
4. Third Person: In some cases, a contract may be performed by a third person provided the promisee accepts the arrangement. According to Section 41 of the Indian Contract Act, once the promisee accepts the performance from a third person, he cannot compel the promisor to perform the contract again. 
5. Performance of Joint Promises: According to section 42 of the Indian Contract Act, when two or more persons have made a joint promise, the joint promisors must fulfill the promise jointly during their lifetime. And if any one of them dies, then his legal representatives and survivors must jointly fulfill the promise. 

Section 43 of the Indian Contract Act further provides that unless a contrary intention appears from the contract, each joint promisor may compel every other joint promisor to contribute equally to the performance of the promise. If any joint promisor makes a default in such contribution, the remaining joint promisors must bear the loss arising from such default in equal shares.

Question:

Aman received a box of chocolates from Basant and promised to pay Rupees 5000. Later on, A becomes bankrupt. Chetan who is a friend of Aman pays rupees 1000 to Besant on behalf of Aman. Aman is not aware of such a transaction. In civil court, insolvency proceedings have started against Aman. Meanwhile, Basant has also applied for a recovery of 5000 rupees. Decide.

Read the passage carefully and answer the question

The Contract should be performed by the promisor himself. However, in certain cases, it can also be performed by his agents or legal representatives. It all depends upon the intention of the parties. Normally a contract can be performed by the following persons. 

1. Promisor himself: If from the nature of the contract it appears that it was the intention of the parties that the promise should be performed by the promisor himself, such promise must be performed by the promisor. This usually applies to contracts involving personal skill, task, or artwork. 
2. Promisor or his Agent: Where the contract does not involve the personal skill of the promisor, the contract could be performed by the promisor himself or by any competent person employed by him for the purpose, 
3. Legal Representatives: The contracts which do not involve any personal skill or taste, may be performed by his legal representative after the death of the promisor.
4. Third Person: In some cases, a contract may be performed by a third person provided the promisee accepts the arrangement. According to Section 41 of the Indian Contract Act, once the promisee accepts the performance from a third person, he cannot compel the promisor to perform the contract again. 
5. Performance of Joint Promises: According to section 42 of the Indian Contract Act, when two or more persons have made a joint promise, the joint promisors must fulfill the promise jointly during their lifetime. And if any one of them dies, then his legal representatives and survivors must jointly fulfill the promise. 

Section 43 of the Indian Contract Act further provides that unless a contrary intention appears from the contract, each joint promisor may compel every other joint promisor to contribute equally to the performance of the promise. If any joint promisor makes a default in such contribution, the remaining joint promisors must bear the loss arising from such default in equal shares.

Question:

K promises to paint a picture for L on a certain day, at a certain price. K dies before the day of the contract. Decide. 

Read the passage carefully and answer the question

The Contract should be performed by the promisor himself. However, in certain cases, it can also be performed by his agents or legal representatives. It all depends upon the intention of the parties. Normally a contract can be performed by the following persons. 

1. Promisor himself: If from the nature of the contract it appears that it was the intention of the parties that the promise should be performed by the promisor himself, such promise must be performed by the promisor. This usually applies to contracts involving personal skill, task, or artwork. 
2. Promisor or his Agent: Where the contract does not involve the personal skill of the promisor, the contract could be performed by the promisor himself or by any competent person employed by him for the purpose, 
3. Legal Representatives: The contracts which do not involve any personal skill or taste, may be performed by his legal representative after the death of the promisor.
4. Third Person: In some cases, a contract may be performed by a third person provided the promisee accepts the arrangement. According to Section 41 of the Indian Contract Act, once the promisee accepts the performance from a third person, he cannot compel the promisor to perform the contract again. 
5. Performance of Joint Promises: According to section 42 of the Indian Contract Act, when two or more persons have made a joint promise, the joint promisors must fulfill the promise jointly during their lifetime. And if any one of them dies, then his legal representatives and survivors must jointly fulfill the promise. 

Section 43 of the Indian Contract Act further provides that unless a contrary intention appears from the contract, each joint promisor may compel every other joint promisor to contribute equally to the performance of the promise. If any joint promisor makes a default in such contribution, the remaining joint promisors must bear the loss arising from such default in equal shares.

Question:

Rohan has agreed to manage the catering services during the marriage of Sohan’s son Ramu. On the day of marriage, Rohan felt ill and sent his manager to the management of catering services. Ramu happily gets married to Tina and people appreciated the food and decoration of the event. When Rohan asked Sohan for the remaining amount, he denied it because Rohan himself had not managed so it is a breach. Decide.

Read the passage and answer the question that follow.

Natural justice is another name for common sense justice rules of natural justice are not in codified form these principles are embedded or ingrained or inbuilt in the conscience of human beings. It supplies the omission made in codified law and helps in the administration of justice. Natural justice is not only confined to ‘fairness’ it will take many shades and colours based on the context. Thus natural justice apart from ‘fairness’ also implies reasonableness, equity and equality. They are neither cast in a rigid mould nor can they be put in a legal straitjacket. These principles written by nature in the heart of mankind, they are immutable, inviolable, and inalienable.

It is true that the concept of natural justice is not very clear and, therefore, it is not possible to define it; yet the principles of natural justice are accepted and enforced. In the case of Ridge V. Baldwin Court observed that “in modern times have sometimes been expressed to the effect that natural justice is as vague as to be practically meaningless. But I would regard these as tainted by the perennial fallacy that because something cannot be cut and dried or nicely weighed or measured therefore it does not exist”. The term natural justice signifies fundamental rules of judicial procedure and fair play in action. According to Lord Widgery “the principles of natural justice were those fundamental rules; the breach will prevent justice from being seen to be done”. Earliest expression of ‘natural justice’ could be found in the philosophical expression of Roman Jurist (jus natural) and signified rules and principles for the conduct of man which were independent of enacted law or customs and could be discovered by the rational intelligence of man and would grow out of and conform to his nature.

The rule against bias that surfaced in 1610 in Dr Bonham's Casewhere Chief Justice Coke went so far as to say that the Court could declare an Act of Parliament void if it made a man as judge in his own cause, or otherwise ‘against common right and reason’. This was one of his grounds for disallowing the claim of the College of Physicians to fine and imprison Doctor Bonham, a Doctor of Physics of Cambridge University, for practising in the city of London without the licence of College of Physicians. The statute under which the College acted provided that fines should go half to the King half to the College so that the College had a financial interest in its own judgement and was judged in its own cause.

Question:

X is a student of a college and his father Y is a professor in the same college. In one instance, X is caught to be involved in unparliamentary activities inside the college campus. The enquiry committee is set up and Y is appointed as the head of the committee. Decide.

Read the passage and answer the question that follow.

Natural justice is another name for common sense justice rules of natural justice are not in codified form these principles are embedded or ingrained or inbuilt in the conscience of human beings. It supplies the omission made in codified law and helps in the administration of justice. Natural justice is not only confined to ‘fairness’ it will take many shades and colours based on the context. Thus natural justice apart from ‘fairness’ also implies reasonableness, equity and equality. They are neither cast in a rigid mould nor can they be put in a legal straitjacket. These principles written by nature in the heart of mankind, they are immutable, inviolable, and inalienable.

It is true that the concept of natural justice is not very clear and, therefore, it is not possible to define it; yet the principles of natural justice are accepted and enforced. In the case of Ridge V. Baldwin Court observed that “in modern times have sometimes been expressed to the effect that natural justice is as vague as to be practically meaningless. But I would regard these as tainted by the perennial fallacy that because something cannot be cut and dried or nicely weighed or measured therefore it does not exist”. The term natural justice signifies fundamental rules of judicial procedure and fair play in action. According to Lord Widgery “the principles of natural justice were those fundamental rules; the breach will prevent justice from being seen to be done”. Earliest expression of ‘natural justice’ could be found in the philosophical expression of Roman Jurist (jus natural) and signified rules and principles for the conduct of man which were independent of enacted law or customs and could be discovered by the rational intelligence of man and would grow out of and conform to his nature.

The rule against bias that surfaced in 1610 in Dr Bonham's Casewhere Chief Justice Coke went so far as to say that the Court could declare an Act of Parliament void if it made a man as judge in his own cause, or otherwise ‘against common right and reason’. This was one of his grounds for disallowing the claim of the College of Physicians to fine and imprison Doctor Bonham, a Doctor of Physics of Cambridge University, for practising in the city of London without the licence of College of Physicians. The statute under which the College acted provided that fines should go half to the King half to the College so that the College had a financial interest in its own judgement and was judged in its own cause.

Question:

Mr X is an employee of a corporate office. His wife Y is a judge. In one instance, X is found to be involved in a money laundering case at his office. The office now files a suit and Y is appointed as the judge for this case. Decide.

Read the passage and answer the question that follow.

Natural justice is another name for common sense justice rules of natural justice are not in codified form these principles are embedded or ingrained or inbuilt in the conscience of human beings. It supplies the omission made in codified law and helps in the administration of justice. Natural justice is not only confined to ‘fairness’ it will take many shades and colours based on the context. Thus natural justice apart from ‘fairness’ also implies reasonableness, equity and equality. They are neither cast in a rigid mould nor can they be put in a legal straitjacket. These principles written by nature in the heart of mankind, they are immutable, inviolable, and inalienable.

It is true that the concept of natural justice is not very clear and, therefore, it is not possible to define it; yet the principles of natural justice are accepted and enforced. In the case of Ridge V. Baldwin Court observed that “in modern times have sometimes been expressed to the effect that natural justice is as vague as to be practically meaningless. But I would regard these as tainted by the perennial fallacy that because something cannot be cut and dried or nicely weighed or measured therefore it does not exist”. The term natural justice signifies fundamental rules of judicial procedure and fair play in action. According to Lord Widgery “the principles of natural justice were those fundamental rules; the breach will prevent justice from being seen to be done”. Earliest expression of ‘natural justice’ could be found in the philosophical expression of Roman Jurist (jus natural) and signified rules and principles for the conduct of man which were independent of enacted law or customs and could be discovered by the rational intelligence of man and would grow out of and conform to his nature.

The rule against bias that surfaced in 1610 in Dr Bonham's Casewhere Chief Justice Coke went so far as to say that the Court could declare an Act of Parliament void if it made a man as judge in his own cause, or otherwise ‘against common right and reason’. This was one of his grounds for disallowing the claim of the College of Physicians to fine and imprison Doctor Bonham, a Doctor of Physics of Cambridge University, for practising in the city of London without the licence of College of Physicians. The statute under which the College acted provided that fines should go half to the King half to the College so that the College had a financial interest in its own judgement and was judged in its own cause.

Question:

X was a renowned cricketer in the 1980s. His son Y is a struggling cricketer who has been trying to get into the national team for many years. In the year 2020, X is appointed as a member of the selection committee. In the match which is supposed to decide the final team of the nation, Y scores a century and Z scores 65 runs. However, Z is selected to represent India and Y is not. Y now appeals against the decision, the main ground being the presence of X in the committee. Decide.

Read the passage and answer the question that follow.

Natural justice is another name for common sense justice rules of natural justice are not in codified form these principles are embedded or ingrained or inbuilt in the conscience of human beings. It supplies the omission made in codified law and helps in the administration of justice. Natural justice is not only confined to ‘fairness’ it will take many shades and colours based on the context. Thus natural justice apart from ‘fairness’ also implies reasonableness, equity and equality. They are neither cast in a rigid mould nor can they be put in a legal straitjacket. These principles written by nature in the heart of mankind, they are immutable, inviolable, and inalienable.

It is true that the concept of natural justice is not very clear and, therefore, it is not possible to define it; yet the principles of natural justice are accepted and enforced. In the case of Ridge V. Baldwin Court observed that “in modern times have sometimes been expressed to the effect that natural justice is as vague as to be practically meaningless. But I would regard these as tainted by the perennial fallacy that because something cannot be cut and dried or nicely weighed or measured therefore it does not exist”. The term natural justice signifies fundamental rules of judicial procedure and fair play in action. According to Lord Widgery “the principles of natural justice were those fundamental rules; the breach will prevent justice from being seen to be done”. Earliest expression of ‘natural justice’ could be found in the philosophical expression of Roman Jurist (jus natural) and signified rules and principles for the conduct of man which were independent of enacted law or customs and could be discovered by the rational intelligence of man and would grow out of and conform to his nature.

The rule against bias that surfaced in 1610 in Dr Bonham's Casewhere Chief Justice Coke went so far as to say that the Court could declare an Act of Parliament void if it made a man as judge in his own cause, or otherwise ‘against common right and reason’. This was one of his grounds for disallowing the claim of the College of Physicians to fine and imprison Doctor Bonham, a Doctor of Physics of Cambridge University, for practising in the city of London without the licence of College of Physicians. The statute under which the College acted provided that fines should go half to the King half to the College so that the College had a financial interest in its own judgement and was judged in its own cause.

Question:

X is a married judge who is well known for his honesty in the entire city. He has a son Y. One fine day Y gets kidnapped and the kidnapper demands a sum of 20 lakhs from X. However, the kidnapper is caught by the police. X is now appointed as the judge for the hearing of the kidnapper. Decide.

Read the passage and answer the question that follow.

Natural justice is another name for common sense justice rules of natural justice are not in codified form these principles are embedded or ingrained or inbuilt in the conscience of human beings. It supplies the omission made in codified law and helps in the administration of justice. Natural justice is not only confined to ‘fairness’ it will take many shades and colours based on the context. Thus natural justice apart from ‘fairness’ also implies reasonableness, equity and equality. They are neither cast in a rigid mould nor can they be put in a legal straitjacket. These principles written by nature in the heart of mankind, they are immutable, inviolable, and inalienable.

It is true that the concept of natural justice is not very clear and, therefore, it is not possible to define it; yet the principles of natural justice are accepted and enforced. In the case of Ridge V. Baldwin Court observed that “in modern times have sometimes been expressed to the effect that natural justice is as vague as to be practically meaningless. But I would regard these as tainted by the perennial fallacy that because something cannot be cut and dried or nicely weighed or measured therefore it does not exist”. The term natural justice signifies fundamental rules of judicial procedure and fair play in action. According to Lord Widgery “the principles of natural justice were those fundamental rules; the breach will prevent justice from being seen to be done”. Earliest expression of ‘natural justice’ could be found in the philosophical expression of Roman Jurist (jus natural) and signified rules and principles for the conduct of man which were independent of enacted law or customs and could be discovered by the rational intelligence of man and would grow out of and conform to his nature.

The rule against bias that surfaced in 1610 in Dr Bonham's Casewhere Chief Justice Coke went so far as to say that the Court could declare an Act of Parliament void if it made a man as judge in his own cause, or otherwise ‘against common right and reason’. This was one of his grounds for disallowing the claim of the College of Physicians to fine and imprison Doctor Bonham, a Doctor of Physics of Cambridge University, for practising in the city of London without the licence of College of Physicians. The statute under which the College acted provided that fines should go half to the King half to the College so that the College had a financial interest in its own judgement and was judged in its own cause.

Question:

X and Y have been married for five years. X is a judge and Y is a doctor. X is pretty much unhappy with his married life so he wants to divorce Y. Y refuses to agree to a divorce by mutual consent hence X files a suit against Y. Decide.

Read the passage and answer the question that follow.

In the case of M/S Halonex Limited, 59-A Noida vs State of U.P., it was held that “In reply to the aforesaid submission, learned counsel for opposite party no.2 submitted that the case of the applicants that no amount is due from their side to the complainant is a matter of defence which cannot be considered at this stage. It has been submitted that the term 'entrustment' as used in Section 405 IPC has been given a wider interpretation. It has been submitted that the goods returned by the complainant to the Company for replacement or for reimbursement would be deemed to have been entrusted to the Company and as the applicants 2 & 3 were handling its affair they become responsible. To buttress the said submission, the learned counsel for the complainant drew the attention of the Court to a decision of the Apex Court in the case of Ram Narayan Popli Vs. Central Bureau of Investigation: (2003) 3 SCC 641, wherein it was observed that: "the term "entrustment" is not necessarily a term of law. It may have different implications in different contexts. In its most general signification all it imports is the handing over possession for some purpose which may not imply the conferring of any proprietary right at all." Attention was also drawn to an observation made in the judgment of the aforesaid case, where it was observed that: "to establish the charge of criminal breach of trust, the prosecution is not obliged to prove the precise mode of conversion, misappropriation or misapplication by the accused of the property entrusted to him or over which he has dominion. The principal ingredient of the offence being dishonest misappropriation or conversion which may not ordinarily be a matter of direct proof, entrustment of property and failure in breach of an obligation to account for the property entrusted if proved, may, in the light of other circumstances, justifiably lead to an inference of dishonest misappropriation or conversion”.

Question:

X tracks down an expensive necklace on the road. Not knowing to whom it belongs. X sells it promptly to a jeweller without attempting to find the owner or submitting the necklace to the authorities. Decide the liability of X.