Sample Problem: If the price of a commodity increases by 20%, by what percentage must a householder reduce its consumption so as not to increase the expenditure?

Solution: Let the original price be 100 and consumption be 100 units (Total cost = 10,000). New price = 120. New consumption to keep cost at 10,000 = 10000 / 120 = 83.33 units. Reduction = 100 - 83.33 = 16.67%.

Sample Problem: Divide 1,200 between A and B in the ratio 3:5. What is B's share?

Solution: Total parts = 3 + 5 = 8. B's share = (5/8) × 1200 = 750.

Sample Problem: A retailer buys a watch for 400 and sells it for 480. Find his profit percentage.

Solution: Profit = 480 - 400 = 80. Profit % = (80 / 400) × 100 = 20%.

Sample Problem: In what ratio must a grocer mix tea at 60/kg and 65/kg so that the mixture is worth 62/kg?

Solution: By the rule of alligation: (Cheaper price : Dearer price) = (65 - 62) : (62 - 60) = 3 : 2.

Sample Problem: A can finish a work in 10 days and B can do it in 15 days. How long will they take to finish it working together?

Solution: A's 1-day work = 1/10, B's 1-day work = 1/15. Combined 1-day work = 1/10 + 1/15 = 5/30 = 1/6. Together they take 6 days.

Sample Problem: A car travels at a speed of 54 km/h. Express its speed in meters per second (m/s).

Solution: To convert km/h to m/s, multiply by 5/18. Speed = 54 × (5/18) = 15 m/s.

Sample Problem: Find the compound interest on 10,000 for 2 years at 10% per annum compounded annually.

Solution: Amount = 10000 × (1 + 10/100)² = 10000 × 1.21 = 12,100. Interest = 12,100 - 10,000 = 2,100.

Sample Problem: What is the least number that must be added to 1056 to make it completely divisible by 23?

Solution: Dividing 1056 by 23 leaves a remainder of 21. The number to be added = 23 - 21 = 2.

Sample Problem: Find the next number in the series: 2, 4, 8, 16, 32, ___.

Solution: Each number is multiplied by 2. The next term is 32 × 2 = 64.

Sample Problem: Evaluate: 20 + 8 × 2 - (6 ÷ 2).

Solution: Apply BODMAS: 20 + 16 - 3 = 36 - 3 = 33.

Sample Problem: Solve for x: 3x + 7 = 22.

Solution: 3x = 22 - 7 => 3x = 15 => x = 5.

Sample Problem: Father is 4 times as old as his son. In 20 years, he will be twice as old as his son. Find the son's present age.

Solution: Let son = x, Father = 4x. In 20 years: 4x + 20 = 2(x + 20) => 4x + 20 = 2x + 40 => 2x = 20 => x = 10.

Sample Problem: In how many ways can a committee of 3 members be selected from a group of 5 people?

Solution: Use combinations: 5C3 = (5×4×3)/(3×2×1) = 10 ways.

Sample Problem: What is the probability of getting a sum of 7 when rolling two fair dice?

Solution: Total outcomes = 36. Favorable outcomes: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 outcomes. Probability = 6/36 = 1/6.

Sample Problem: Find the volume of a cylinder with a radius of 7 cm and a height of 10 cm. (Take π = 22/7)

Solution: Volume = πr²h = (22/7) × 7 × 7 × 10 = 1540 cm³.

Sample Problem: Two angles of a triangle are 50° and 70°. Find the third angle.

Solution: Sum of angles in a triangle is 180°. Third angle = 180° - (50° + 70°) = 60°.

Sample Problem: If a pie chart shows that a company spends 25% of its 1,00,000 budget on marketing, what is the exact marketing spend?

Solution: Marketing spend = 25% of 100000 = 0.25 × 100000 = 25,000.

Sample Problem: Find the median of the data set: 5, 11, 3, 9, 7.

Solution: Arrange in ascending order: 3, 5, 7, 9, 11. The middle value (median) is 7.

Sample Problem: If sin θ = 3/5, find the value of tan θ.

Solution: sin θ = Perpendicular / Hypotenuse. By Pythagoras theorem, Base = √(5² - 3²) = 4. Therefore, tan θ = Perpendicular / Base = 3/4.

Sample Problem: Solve the inequality: 5x - 3 > 12.

Solution: 5x > 12 + 3 => 5x > 15 => x > 3.

Sample Problem: Find the next term in the series: A1Z, C3X, E5V, G7T, ___

Solution: The letters follow the first, third, fifth, and seventh positions of the alphabet forward and backward. The numbers increase by 2. The next term is I9R.

Sample Problem: Pointing to a photograph, a man said, "I have no brother or sister, but that man's father is my father's son." Whose photograph was it?

Solution: "My father's son" while having no siblings means the man himself. Since this person is "that man's father", the photograph is of his own son.

Sample Problem: If in a certain code language, 'ROSE' is written as 'TQUG', how is 'BISCUIT' written in that code?

Solution: Each letter is moved two places forward (+2) in the alphabetical order. Following this rule, 'BISCUIT' becomes DKUEWKV.

Sample Problem: Is X an integer? Statement 1: 2X is an integer. Statement 2: X/2 is an integer.

Solution: Statement 1 alone is insufficient. Statement 2 alone is sufficient because if a number divided by 2 is an integer, the number itself must be an integer.

Sample Problem: A man walks 3 km North, then turns right and walks 4 km. How far is he from his starting point?

Solution: The path forms a right-angled triangle. Using the Pythagorean theorem: Distance = √(3² + 4²) = √25 = 5 km.

Sample Problem: What is the mirror image of the word 'BOAT' when the mirror is placed to its right?

Solution: The letters reverse their order and left-right orientation. The resulting reflection appears as TAOB (with each individual letter flipped horizontally).

Sample Problem: Statement: Most software engineers in Company X are creative. Rajesh is a software engineer in Company X. Conclusion: Rajesh is definitely creative. Is this conclusion true?

Solution: No. The statement uses 'Most', not 'All'. Therefore, we cannot conclusively say that Rajesh is definitely creative.

Sample Problem: Statements: All pens are markers. Some markers are scales. Conclusion: Some pens are scales. Does this follow?

Solution: No. There is no definite overlapping region established between 'pens' and 'scales' through the common connection of 'markers'.

Sample Problem: A, B, C, and D are sitting in a row facing North. A is to the immediate left of B. C is between B and D. Who is at the left end?

Solution: Following the clues, the layout from left to right must be A, B, C, D. Thus, A is at the left end.

Sample Problem: Find the angle between the hour hand and the minute hand of a clock at 3:40.

Solution: Using the formula Angle = |30H - 5.5M|: Angle = |30(3) - 5.5(40)| = |90 - 220| = 130°.

Sample Problem: A candidate meets all criteria for a job except age, but has 5 years of extra experience. The rule states such cases go to the Director. What is the action?

Solution: The candidate must be referred to the Director.

Sample Problem: Rahul ranks 10th from the top and 15th from the bottom in a class. How many students are there in total?

Solution: Total = (Position from top + Position from bottom) - 1 = (10 + 15) - 1 = 24 students.

Sample Problem: In a 3x3 grid, row 1 is [2, 4, 8], row 2 is [3, 9, 27]. What are the first two numbers of row 3 if it follows the same pattern?

Solution: The pattern is x, x², x³. If row 3 starts with 4, the sequence will be 4, 16, 64.

Sample Problem: Statement: The city has seen a massive surge in dengue cases. Action: The civic body should conduct immediate fumigation drives. Is the action course valid?

Solution: Yes. The action directly addresses the root cause (mosquito breeding) of the stated problem.

Sample Problem: If Input is 'day 42 night 15' and Step 1 is 'day 15 42 night' (sorting numbers ascending and words alphabetical), what is Step 2?

Solution: The next smallest number or word is processed. Step 2 becomes: day 15 night 42.

Sample Problem: A square paper is folded diagonally, and a single hole is punched in the center. How many holes appear when opened?

Solution: Since the punch passes through the folded layer, it unfolds to reveal one central hole.

Sample Problem: Five lectures (P, Q, R, S, T) are held Monday to Friday. R is on Monday. T is immediately after S. Q is on Friday. When is P held?

Solution: R is Mon, Q is Fri. S and T must be consecutive (Tue and Wed). Therefore, P must be held on Thursday.

Sample Problem: Three friends X, Y, and Z wear Red, Blue, and Green shirts. X does not wear Red. Y does not wear Blue or Red. What color does Z wear?

Solution: Since Y doesn't wear Blue or Red, Y wears Green. Since X doesn't wear Red and Green is taken, X wears Blue. Therefore, Z must wear Red.

Sample Problem: Find the Synonym of Candid and the Antonym of Obscure.

Solution: Synonym of Candid is Frank (or Honest). Antonym of Obscure is Clear (or Distinct).

Sample Problem: The government decided to ________ the old law to make room for new digital regulations. (Options: revoke, invoke, provoke, evict)

Solution: revoke (meaning to officially cancel or repeal a law).

Sample Problem: Neither the teacher (A) / nor the students (B) / was present in the staff room. (C) / No error (D)

Solution: (C). According to the rule of proximity, when subjects are joined by 'neither/nor', the verb agrees with the closer subject ('students'), so 'was' should be changed to 'were'.

Sample Problem: Architect : Building :: Sculptor : ________

Solution: Statue (An architect creates a building; a sculptor creates a statue).

Sample Problem: Correct the underlined part: He *has been working* here since five years.

Solution: Change to 'is working' or 'has been working for'. Since a duration of time ('five years') is given, the preposition 'for' must replace 'since'.

Sample Problem: If a text discusses a city's failing drainage system using words like 'negligent', 'disastrous', and 'apathetic', what is the author's tone?

Solution: Critical or Cynical (reflecting disapproval and frustration).

Sample Problem: Rearrange: (A) Then he opened the door. (B) Rahul walked up the stairs. (C) He looked for his keys.

Solution: B-C-A (Rahul walking up is the opening action, looking for keys follows, and opening the door is the result).

Sample Problem: Convert to Indirect Speech: She said, 'I am writing an essay now.'

Solution: She said that she was writing an essay then.

Sample Problem: What is the meaning of the word Pragmatic?

Solution: Practical (dealing with things sensibly and realistically based on practical rather than theoretical considerations).

Sample Problem: The weather was severe, ________ we decided to stay indoors to avoid the storm. (Options: but, because, so, although)

Solution: so (indicates a cause-and-effect relationship).

Sample Problem: What does the idiom “Burn the midnight oil” mean?

Solution: To study or work late into the night.

Sample Problem: 'Sales increased after we ran a digital ad. Therefore, the ad caused the sales boost.' What is the flaw?

Solution: It assumes correlation proves causation, ignoring other factors like seasonal demand or competitor price changes.

Sample Problem: Arrange in dictionary order: 1. Absolute, 2. Abstract, 3. Absolve, 4. Absence.

Solution: 4-1-3-2 (Absence, Absolute, Absolve, Abstract).

Sample Problem: What is a single word for 'A person who looks at the bright side of things'?

Solution: Optimist.

Sample Problem: Convert to Passive Voice: 'The chef prepared a delicious meal.'

Solution: 'A delicious meal was prepared by the chef.'

Sample Problem: Choose the correct spelling: (A) Comittee, (B) Committee, (C) Commitee, (D) Comitee

Solution: (B) Committee (contains double 'm', double 't', and double 'e').