Quantitative Aptitude PYQs

Shortcut Trick

Solve the bracket and multiplication first: (37 + 19) × 2 = 56 × 2 = 112.

Group all positive terms: 95 + 62 + 112 = 269.

Group all negative terms: −69 − 103 = −172.

Final calculation: 269 − 172 = 97.

∴ The correct answer is 97.

Alternate Method

Given: 95 + 62 − 69 + (37 + 19) × 2 − 103

Method Used: Apply the BODMAS rule (Brackets, Of, Division, Multiplication, Addition, Subtraction).

⇒ 95 + 62 − 69 + (56) × 2 − 103 (Solving Brackets)

⇒ 95 + 62 − 69 + 112 − 103 (Solving Multiplication)

⇒ 157 − 69 + 112 − 103 (Solving Addition from left)

⇒ 88 + 112 − 103 (Solving Subtraction)

⇒ 200 − 103 (Solving Addition)

⇒ 97

∴ The correct answer is 97.

Additional Information

BODMAS Rule

It defines the order of operations: Brackets (), Of, Division (÷), Multiplication (×), Addition (+), and Subtraction (−).

Types of Brackets

Solve in the order of: Bar/Vinculum, then Parentheses (), then Curly braces {}, and finally Square brackets [].

Addition and Subtraction Priority

Addition and subtraction have the same priority and can be solved from left to right or by grouping terms with similar signs.

Shortcut Trick

Solve using BODMAS: Identify Of, Division, and Multiplication first.

96 − 27 + (14 × 2) + (39 ÷ 3) − (28 × 2) + 17

⇒ 96 − 27 + 28 + 13 − 56 + 17

⇒ (96 + 28 + 13 + 17) − (27 + 56) = 154 − 83 = 71

∴ The correct answer is 71.

Alternate Method

Given: 96 − 27 + 14 × 2 + 39 ÷ 3 − (28 of 2) + 17

Method Used: BODMAS Rule (Bracket, Of, Division, Multiplication, Addition, Subtraction)

⇒ 96 − 27 + 14 × 2 + 39 ÷ 3 − 56 + 17 (Solving Of: 28 × 2)

⇒ 96 − 27 + 14 × 2 + 13 − 56 + 17 (Solving Division: 39 ÷ 3)

⇒ 96 − 27 + 28 + 13 − 56 + 17 (Solving Multiplication: 14 × 2)

⇒ (96 + 28 + 13 + 17) − (27 + 56) (Grouping Positive and Negative terms)

⇒ 154 − 83

⇒ 71

∴ The correct answer is 71.

Additional Information

BODMAS / VBODMAS Rule

This mnemonic helps remember the order of operations: Vinculum, Brackets, Of, Division, Multiplication, Addition, and Subtraction.

Importance of 'Of'

The Of operation is mathematically treated as multiplication but holds higher priority than division and regular multiplication in a sequence.

Grouping Strategy

To avoid calculation errors in long series, always group all positive numbers and all negative numbers separately before the final subtraction.

Shortcut Trick

Check divisibility by HCF (18): Only option (4) contains numbers where both 90 and 108 are multiples of 18.

Verify Sum: 90 + 108 = 198 (Matches the condition).

Verify LCM: Numbers are 18×5 and 18×6 ⇒ LCM = 18 × 5 × 6 = 540 (Matches the condition).

∴ The correct answer is 90 and 108.

Alternate Method

Given: HCF = 18, LCM = 540, Sum = 198.

Formula Used: Product of numbers = HCF × LCM | Numbers can be assumed as Ha and Hb (where H is HCF and a, b are co-primes).

⇒ Let the numbers be 18a and 18b.

⇒ 18a + 18b = 198 ⇒ 18(a + b) = 198

⇒ a + b = 198 ÷ 18 = 11

⇒ LCM = 18 × a × b = 540

⇒ ab = 540 ÷ 18 = 30

⇒ We need two co-prime numbers whose sum is 11 and product is 30.

⇒ Solving x² − 11x + 30 = 0 ⇒ (x − 5)(x − 6) = 0

⇒ a = 5 and b = 6

⇒ Number 1 = 18 × 5 = 90

⇒ Number 2 = 18 × 6 = 108

∴ The correct answer is 90 and 108.

Additional Information

Product Property

For any two numbers A and B, the relationship is: A × B = HCF(A, B) × LCM(A, B).

Co-prime Factorization

If H is the HCF of two numbers, the numbers can be written as H × x and H × y, where HCF(x, y) = 1.

LCM of Multiples

The LCM of two numbers Hx and Hy (where H is the HCF) is H × x × y.

Shortcut Trick

Use the Algebraic Identity: (a⁴ − b⁴) ÷ (a² − b²) = a² + b².

Here, let a = 0.7 and b = 0.3.

Required value = (0.7)² + (0.3)²

⇒ 0.49 + 0.09 = 0.58.

∴ The correct answer is 0.58.

Alternate Method

Given:

Expression = ((0.7)⁴ − (0.3)⁴) / ((0.7)² − (0.3)²)

Formula Used:

Difference of Squares: x² − y² = (x − y)(x + y)

⇒ Let a = 0.7 and b = 0.3.

⇒ The numerator is in the form a⁴ − b⁴, which can be written as (a²)² − (b²)².

⇒ Applying the formula to the numerator: (a²)² − (b²)² = (a² − b²)(a² + b²).

⇒ Expression = [(a² − b²)(a² + b²)] ÷ (a² − b²).

⇒ By cancellation of common terms, the expression simplifies to: a² + b².

⇒ Value = (0.7)² + (0.3)²

⇒ Value = 0.49 + 0.09

⇒ Value = 0.58.

∴ The correct answer is 0.58.

Additional Information

Algebraic Identities

Standard identities like a² − b² = (a − b)(a + b) and a² + b² = (a + b)² − 2ab are frequently used in Simplification problems.

Power Rules

The rule (x^m)ⁿ = x^m×n allows us to convert high-order powers like x⁴ or x⁶ into squared or cubed forms for easier calculation.

Decimal Calculations

When squaring a decimal, the number of decimal places doubles. For example, (0.1)² = 0.01 and (0.01)² = 0.0001.

Shortcut Trick

Solve the square roots first: 10 ÷ 5 + 8.

According to BODMAS, perform division before addition: 2 + 8 = 10.

The required value of 2x is 2 × 10 = 20.

∴ The correct answer is 20.

Alternate Method

Given: x = √100 ÷ √25 + √64

Formula: Apply the BODMAS rule (Division, then Addition).

⇒ x = 10 ÷ 5 + 8

⇒ x = 2 + 8

⇒ x = 10

Now, we need to find the value of 2x:

⇒ 2x = 2 × 10

⇒ 2x = 20

∴ The correct answer is 20.

Additional Information

BODMAS Rule

It defines the order of operations: Brackets, Orders (powers/roots), Division, Multiplication, Addition, and Subtraction.

Perfect Squares

A perfect square is a number that can be expressed as the product of two equal integers. For example, 10 × 10 = 100, so √100 = 10.

Square Root Properties

For any positive numbers a and b, √a ÷ √b = √(a ÷ b). In this case, √100 ÷ √25 = √(100 ÷ 25) = √4 = 2.

Shortcut Trick

First, calculate the square root of 20.25: √20.25 = 4.5.

Subtract 4.5 from the total sum: √(16 + x) = 9.5 − 4.5 = 5.

Square both sides to find the value inside the root: 16 + x = 5² = 25.

Solve for x: x = 25 − 16 = 9.

∴ The correct answer is 9.

Alternate Method

Given:

√20.25 + √(16 + x) = 9.5

Calculation:

⇒ √(2025/100) + √(16 + x) = 9.5

⇒ 45/10 + √(16 + x) = 9.5

⇒ 4.5 + √(16 + x) = 9.5

⇒ √(16 + x) = 9.5 − 4.5

⇒ √(16 + x) = 5

⇒ 16 + x = 5² (Squaring both sides)

⇒ 16 + x = 25

⇒ x = 25 − 16

⇒ x = 9

∴ The correct answer is 9.

Additional Information

Square Root of Decimal Numbers

To find the square root of a decimal, convert it to a fraction with a power of 10 in the denominator, or calculate √N and adjust the decimal point (e.g., √20.25 = √2025 ÷ 10).

Squaring Rule

If √A = B, then A = B². This property is used to eliminate radical signs in algebraic equations.

Perfect Square Shortcut (Ending in 25)

The square root of a number ending in 25 always ends in 5. For 2025, since 4 × 5 = 20, the root is 45.

Shortcut Trick

Recognize the standard Pythagorean triplet: 5, 12, 13.

In a rectangle, the diagonal acts as the hypotenuse (13 cm).

Since the given length is 5 cm, the breadth must be 12 cm.

Ratio of length to breadth = 5 : 12.

∴ The correct answer is 5 : 12.

Alternate Method

Given:

Length (l) = 5 cm

Diagonal (d) = 13 cm

Formula Used:

In a rectangle, d² = l² + b² (by Pythagorean theorem)

Calculations:

⇒ 13² = 5² + b²

⇒ 169 = 25 + b²

⇒ b² = 169 − 25

⇒ b² = 144

⇒ b = √144 = 12 cm

⇒ Ratio = Length : Breadth

⇒ Ratio = 5 : 12

∴ The correct answer is 5 : 12.

Additional Information

Area of Rectangle

The total space occupied by the rectangle is given by Length × Breadth.

Perimeter of Rectangle

The total boundary length of the rectangle is 2 × (Length + Breadth).

Pythagorean Triplets

Common sets of integers that satisfy a² + b² = c² include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).

Shortcut Trick

Semi-perimeter (L + B) = 160 ÷ 2 = 80 m

Given difference (L − B) = 8 m

Length (L) = (Sum + Difference) ÷ 2 = (80 + 8) ÷ 2 = 44 m

Breadth (B) = (Sum − Difference) ÷ 2 = (80 − 8) ÷ 2 = 36 m

Area = L × B = 44 × 36 = 1584 m²

∴ The correct answer is 1584 m².

Alternate Method

Given:

Perimeter of rectangle = 160 m

Difference between length (L) and breadth (B) = 8 m

Formula Used:

Perimeter = 2 × (L + B)

Area = L × B

Calculations:

⇒ 2 × (L + B) = 160

⇒ L + B = 80 — (Eq. 1)

⇒ L − B = 8 — (Eq. 2)

Adding (Eq. 1) and (Eq. 2):

⇒ 2L = 88

⇒ L = 44 m

Subtracting (Eq. 2) from (Eq. 1):

⇒ 2B = 72

⇒ B = 36 m

Calculating the Area:

⇒ Area = 44 × 36

⇒ Area = 1584 m²

∴ The correct answer is 1584 m².

Additional Information

Diagonal of a Rectangle

The distance between opposite corners is given by d = √(L² + B²).

Square with Same Perimeter

For a fixed perimeter, the shape with the maximum area is a square where L = B.

Relation between L+B and L-B

(L + B)² − (L − B)² = 4 × L × B = 4 × Area.

Shortcut Trick

When a number is removed and the average increases, the removed number is always less than the original average.

Total Increase = Count of remaining numbers × Increase in average

Total Increase = 7 × 2 = 14

Removed Number = Original Average − Total Increase = P − 14

∴ The correct answer is P − 14.

Alternate Method

Given: Average of 8 numbers = P. After removing 1 number, the average of 7 numbers = P + 2.

Formula Used: Sum of observations = Average × Total count of observations

⇒ Sum of original 8 numbers = 8 × P = 8P

⇒ Sum of remaining 7 numbers = 7 × (P + 2) = 7P + 14

⇒ Removed number = (Sum of 8 numbers) − (Sum of 7 numbers)

⇒ Removed number = 8P − (7P + 14)

⇒ Removed number = 8P − 7P − 14 = P − 14

∴ The correct answer is P − 14.

Additional Information

Basic Average Formula

Average = (Sum of all observations) ÷ (Total number of observations).

Effect of Removal on Average

If the removed value is equal to the average, the average remains unchanged. If it is less than the average, the average increases.

Net Deviation Rule

The sum of deviations of all items from their arithmetic mean is always zero. This concept helps in solving complex average problems quickly.

Shortcut Trick

Use the formula for the sum of squares of the first n natural numbers: Sum = [n(n + 1)(2n + 1)] ÷ 6

Here, n = 60.

Sum = [60 × (60 + 1) × (2 × 60 + 1)] ÷ 6

Sum = 10 × 61 × 121 = 73810

∴ The correct answer is 73810.

Alternate Method

Given: The series is 1² + 2² + 3² + ...... + 60²

Formula Used: Sum of squares of first n natural numbers = [n × (n + 1) × (2n + 1)] ÷ 6

⇒ Number of terms, n = 60

⇒ Sum = [60 × (60 + 1) × (2 × 60 + 1)] ÷ 6

⇒ Sum = [60 × 61 × 121] ÷ 6

⇒ Sum = 10 × 61 × 121

⇒ Sum = 10 × 7381

⇒ Sum = 73810

∴ The correct answer is 73810.

Additional Information

Sum of first n natural numbers

The formula for the sum of the first n natural numbers is n(n + 1) ÷ 2.

Sum of cubes of first n natural numbers

The formula for the sum of cubes of the first n natural numbers is [n(n + 1) ÷ 2]².

Sum of first n odd numbers

The sum of the first n odd natural numbers is calculated as n².

Sum of first n even numbers

The sum of the first n even natural numbers is given by the formula n(n + 1).

Shortcut Trick

For consecutive natural numbers, the average is always the middle term of the series.

For 23 numbers, the middle term is the 12^th number.

The last 11 numbers are from the 13^th to the 23^rd position; their middle term is the 18^th number.

Given 18^th number = 34 ⇒ 12^th number = 18^th number − (18 − 12) = 34 − 6 = 28.

∴ The correct answer is 28.

Alternate Method

Given: Total numbers = 23; Numbers are consecutive natural numbers in ascending order; Average of last 11 numbers = 34.

Formula: Average of an Arithmetic Progression (AP) = (First term + Last term) ÷ 2

Let the 23 consecutive numbers be x, x+1, x+2, ..., x+22.

⇒ The last 11 numbers are: (x+12), (x+13), ..., (x+22).

⇒ Average of last 11 = [(x + 12) + (x + 22)] ÷ 2

⇒ 34 = (2x + 34) ÷ 2

⇒ 34 = x + 17

⇒ x = 34 − 17 = 17

⇒ Average of all 23 numbers = [First term + Last term] ÷ 2

⇒ Average = [x + (x + 22)] ÷ 2 = x + 11

⇒ Average = 17 + 11 = 28

∴ The correct answer is 28.

Additional Information

Average of Arithmetic Progression

For any series in AP, the average is always the mean of the first and last terms: Average = (a + l) ÷ 2.

Middle Term Rule

If the number of terms (n) is odd, the average is the (n + 1)/2^th term. If n is even, it is the mean of the two middle terms.

Sum of Natural Numbers

The sum of the first n natural numbers is given by the formula S = [n × (n + 1)] ÷ 2.

Shortcut Trick

To find the time when they meet again at the starting point, calculate the Least Common Multiple (LCM) of their individual round times.

LCM(180, 270, 360) = 1080 seconds.

Required time in minutes = 1080 ÷ 60 = 18 minutes.

∴ The correct answer is 18 min.

Alternate Method

Given:

Time taken by A = 180 seconds

Time taken by B = 270 seconds

Time taken by C = 360 seconds

Formula Used:

Time to meet at starting point = LCM of (Time taken by each person to complete one round)

Calculations:

⇒ Prime factors of 180 = 2² × 3² × 5

⇒ Prime factors of 270 = 2 × 3³ × 5

⇒ Prime factors of 360 = 2³ × 3² × 5

⇒ LCM = 2³ × 3³ × 5 = 8 × 27 × 5 = 1080 seconds

⇒ To convert seconds to minutes, divide by 60:

⇒ Time = 1080 ÷ 60 = 18 minutes

∴ The correct answer is 18 min.

Additional Information

Circular Track Meeting Points

When starting together, the time to meet at the starting point is the LCM of individual round times, whereas the time to meet anywhere on the track involves relative speed.

LCM and HCF Property

For any two numbers x and y: LCM(x, y) × HCF(x, y) = x × y. This is useful for cross-verifying factors.

Unit Conversion

Always ensure all values are in the same unit before calculating LCM. 1 minute = 60 seconds.

Shortcut Trick

According to the Unitary Method:

20% of the Mixture = 120 kg

1% of the Mixture = 120 ÷ 20 = 6 kg

100% of the Mixture = 6 × 100 = 600 kg

∴ The correct answer is 600 kg.

Alternate Method

Given:

Percentage of Element A = 20%

Required weight of Element A = 120 kg

Let the total weight of the mixture be x kg.

Formula Used:

Weight of Element = (Percentage ÷ 100) × Total Weight

⇒ 120 = (20 ÷ 100) × x

⇒ 120 = (1 ÷ 5) × x

⇒ x = 120 × 5

⇒ x = 600 kg

∴ The correct answer is 600 kg.

Additional Information

Percentage Change

Percentage increase or decrease is calculated as: (Difference ÷ Original Value) × 100.

Fraction to Percentage

To convert any fraction to a percentage, multiply it by 100. For example, 1/5 × 100 = 20%.

Base Change Rule

If A is x% more than B, then B is [x ÷ (100 + x)] × 100% less than A.

Shortcut Trick

Treat Cost Price (CP) as 100 units.

Since Profit Percentage is 30%, Selling Price (SP) = 100 + 30 = 130 units.

Given 100 units = ₹6800 ⇒ 1 unit = 68.

Selling Price = 130 units = 130 × 68 = ₹8840.

∴ The correct answer is ₹8840.

Alternate Method

Given:

Cost Price (CP) = ₹6800

Profit Percentage (P%) = 30%

Formula Used:

Selling Price (SP) = CP + Profit

Profit = (Profit % ÷ 100) × CP

Calculations:

⇒ Profit = (30 ÷ 100) × 6800

⇒ Profit = 0.3 × 6800

⇒ Profit = ₹2040

⇒ SP = 6800 + 2040

⇒ SP = ₹8840

∴ The correct answer is ₹8840.

Additional Information

Profit and Loss Percentages

Profit % = (Profit ÷ CP) × 100 and Loss % = (Loss ÷ CP) × 100. Both are always calculated on Cost Price.

Marked Price and Discount

Selling Price can also be calculated as Marked Price (MP) − Discount. Discount is always calculated on the Marked Price.

Basic SP Relation

SP = CP × (100 ± Profit/Loss %) ÷ 100. Use (+) for profit and (−) for loss.

Shortcut Trick

Ratio of Cost Price (CP) to Selling Price (SP):

20% of CP = 25% of SP ⇒ CP / SP = 25 / 20 = 5 / 4

Loss = 5 − 4 = 1 unit on a CP of 5 units.

Loss % = (1 / 5) × 100 = 20%

∴ The correct answer is 20%.

Alternate Method

Given:

20% of Cost Price (CP) = 25% of Selling Price (SP)

Formula Used:

Loss Percentage = [(CP − SP) / CP] × 100

Calculations:

⇒ 20/100 × CP = 25/100 × SP

⇒ 20 × CP = 25 × SP

⇒ CP / SP = 25 / 20

⇒ CP / SP = 5 / 4

⇒ Let CP = 5 units and SP = 4 units

⇒ Loss = CP − SP = 5 − 4 = 1 unit

⇒ Loss Percentage = (1 / 5) × 100

⇒ Loss Percentage = 20%

∴ The correct answer is 20%.

Additional Information

Profit Percentage

Profit occurs when SP > CP. Formula: Profit% = [(SP − CP) / CP] × 100.

Relation with Marked Price

Selling Price = Marked Price − Discount. Also, CP × (100 + Profit%) = MP × (100 − Discount%).

Fraction to Percentage Conversion

Standard fractions: 1/4 = 25%, 1/5 = 20%, 1/6 = 16.66%, 1/8 = 12.5%.

Shortcut Trick

Let A = 100 units.

B is 30% more than A ⇒ B = 130 units.

C is 20% less than B ⇒ C = 130 − (20% of 130) = 104 units.

Required percentage = (A ÷ C) × 100 = (100 ÷ 104) × 100.

Calculation ⇒ 96.15%.

∴ The correct answer is 96.15%.

Alternate Method

Given:

Relation between A and B: B = 1.3 × A

Relation between B and C: C = 0.8 × B

Formula Used:

Percentage = (Value ÷ Base Value) × 100

Calculations:

⇒ Express C in terms of A: C = 0.8 × (1.3 × A)

⇒ C = 1.04 × A

⇒ We need to find A as a percentage of C: (A ÷ C) × 100

⇒ Required Percentage = (A ÷ 1.04A) × 100

⇒ Required Percentage = 100 ÷ 1.04 = 96.1538...

⇒ Required Percentage ≈ 96.15%

∴ The correct answer is 96.15%.

Additional Information

Successive Percentage Changes

When a value is changed by x% and then y%, the net change is [x + y + (xy ÷ 100)]%. This is useful for finding the direct relationship between the first and last variables.

Base Value Identification

In percentage comparison, the term after 'than' or 'of' acts as the reference base and is placed in the denominator of the fraction.

Fraction to Percentage Conversion

Memorizing common fractions (like 1/13 ≈ 7.69% or 1/4 = 25%) helps in speeding up competitive exam calculations involving complex ratios.

Shortcut Trick

Time taken by S for 1 full work = 16 × 3 ÷ 2 = 24 days.

Since R is 4 times as efficient as S, the time taken by R will be 1/4^th of the time taken by S.

Days taken by R = 24 ÷ 4 = 6 days.

∴ The correct answer is 6 days.

Alternate Method

Given:

Work done by S = 2/3 part in 16 days.

Efficiency of R = 4 × Efficiency of S.

Formula Used:

Total Work = Efficiency × Time

Calculations:

⇒ Time taken by S to complete full work = 16 × (3 ÷ 2) = 24 days.

⇒ Let efficiency of S = 1 unit/day.

⇒ Total work = Efficiency of S × Time taken by S = 1 × 24 = 24 units.

⇒ Efficiency of R = 4 × Efficiency of S = 4 × 1 = 4 units/day.

⇒ Time taken by R alone = Total work ÷ Efficiency of R

⇒ Time taken by R = 24 ÷ 4 = 6 days.

∴ The correct answer is 6 days.

Additional Information

Work-Efficiency Relationship

Efficiency is inversely proportional to the time taken to complete a work. If the ratio of efficiency of A and B is x : y, then the ratio of time taken by them is y :

x. Work and Wages

Wages are distributed in the ratio of the work done or in the ratio of the efficiencies if the people work for the same amount of time.

Combined Work Formula

If A can do a work in x days and B can do it in y days, then together they can do it in (x × y) ÷ (x + y) days.

Shortcut Trick

Use the MDH rule for proportionality: M₁ × D₁ × H₁ = M₂ × D₂ × H₂

Substitute: 40 × 50 × 9 = M₂ × 75 × 6

18000 = M₂ × 450

M₂ = 18000 ÷ 450 = 40 men

∴ The correct answer is 40 men.

Alternate Method

Given: Initial 40 men can build a wall in 50 days working 9 hours per day. We need to find men required for 75 days working 6 hours per day.

Formula Used: Total Work (Man-Hours) = Men × Days × Hours

⇒ Total work in man-hours = 40 × 50 × 9 = 18,000 units

⇒ Total capacity needed in Case 2 = 75 days × 6 hours = 450 hours per man

⇒ Number of men (M₂) = Total work ÷ Total capacity per man

⇒ M₂ = 18,000 ÷ 450

⇒ M₂ = 40

∴ The correct answer is 40 men.

Additional Information

MDH Rule (Chain Rule)

The general formula is (M₁ × D₁ × H₁ × E₁) ÷ W₁ = (M₂ × D₂ × H₂ × E₂) ÷ W₂, where M is men, D is days, H is hours, E is efficiency, and W is work.

Inverse Variation

Number of men is inversely proportional to the number of days and hours required. If we increase the number of days or hours, fewer men are needed for the same work.

Unit of Work

When the same wall is mentioned, W₁ = W₂, which allows us to equate the products of men, days, and hours directly.

Shortcut Trick

In opposite direction, relative speed is the sum of speeds of both trains.

Relative Speed = (Length of Train A + Length of Train B) ÷ Time

Total Speed = (500 + 200) ÷ 35

Total Speed = 700 ÷ 35 = 20 m/s

∴ The correct answer is 20 m/s.

Alternate Method

Given:

Length of Train A (L_A) = 500 m

Length of Train B (L_B) = 200 m

Time taken to cross (T) = 35 seconds

Formula Used:

Relative Speed (in opposite direction) = Total Distance ÷ Total Time

Calculations:

⇒ Total Distance = L_A + L_B

⇒ Total Distance = 500 + 200 = 700 m

⇒ Total Speed (V_A + V_B) = Total Distance ÷ Time

⇒ Total Speed = 700 ÷ 35

⇒ Total Speed = 20 m/s

∴ The correct answer is 20 m/s.

Additional Information

Relative Speed in Same Direction

When two objects move in the same direction, the relative speed is the difference of their speeds: V_rel = |V₁ − V₂|.

Unit Conversion (km/h to m/s)

To convert speed from km/h to m/s, multiply the value by 5/18. For example, 72 km/h = 72 × (5/18) = 20 m/s.

Crossing a Stationary Object

When a train crosses a stationary pole or man, the distance covered is equal to the length of the train itself.

Shortcut Trick

Convert Speed to metres per minute: 10 km/hr = (10 × 1000) ÷ 60 = 500/3 m/min.

Time taken to cross a stationary man = Length of Train ÷ Speed.

Time = 250 ÷ (500/3) = 250 × 3 ÷ 500 = 3/2 min.

∴ The correct answer is 3/2 min.

Alternate Method

Given:

Length of train (L) = 250 m

Speed of train (v) = 10 km/hr

Formula:

Time = Distance ÷ Speed

Calculations:

⇒ Speed in m/s = 10 × (5/18) = 50/18 = 25/9 m/s

⇒ Time (in sec) = 250 ÷ (25/9)

⇒ Time = 250 × 9 ÷ 25

⇒ Time = 10 × 9 = 90 seconds

⇒ Time (in min) = 90 ÷ 60

⇒ Time = 3/2 minutes

∴ The correct answer is 3/2 min.

Additional Information

Unit Conversion

To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.

Crossing Stationary Objects

When a train crosses a point object (man, pole, tree), the distance covered equals the length of the train.

Crossing Lengthy Objects

When a train crosses a platform or bridge, the distance covered equals (Length of Train + Length of Platform).

Relative Speed

If two objects move in the same direction, Relative Speed = S₁ − S₂. If in opposite directions, Relative Speed = S₁ + S₂.