Quantitative Aptitude PYQs

Shortcut Trick

New person age = New Average + (Previous Total Members × Increase in Average)

Here, Previous Members = 32, New Average = 22, Increase = 22 − 21 = 1

⇒ Teacher age = 22 + (32 × 1)

⇒ 22 + 32 = 54 years

∴ The correct answer is 54 years.

Alternate Method

Given:

Number of students = 32

Average age of students = 21 years

Total members after teacher is included = 32 + 1 = 33

New average age = 22 years

Formula Used:

Sum of observations = Average × Number of observations

Calculations:

⇒ Total age of 32 students = 32 × 21 = 672 years

⇒ Total age of 33 persons (including teacher) = 33 × 22 = 726 years

⇒ Age of the teacher = Total age (33 persons) − Total age (32 students)

⇒ Age of the teacher = 726 − 672

⇒ Age of the teacher = 54 years

∴ The correct answer is 54 years.

Additional Information

Weighted Average Formula

Used to find the average of combined groups: Avg_combined = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂).

Net Deviation Method

The sum of deviations from the average is always zero. Addition of a person with age higher than average increases the overall average.

Arithmetic Mean Properties

If every value in a set is increased by a constant 'k', the average also increases by 'k'.

Shortcut Trick

Net change percentage = a + b + (a × b) ÷ 100

Here, markup percentage (a) = +5% and discount percentage (b) = −40%.

Net change = 5 − 40 + (5 × −40) ÷ 100 = −35 − 2 = −37%.

Negative sign indicates a loss of 37%.

∴ The correct answer is 37%.

Alternate Method

Given: Markup = 5%, Discount = 40%.

Formulas: MP = CP × (100 + Markup%) ÷ 100 | SP = MP × (100 − Discount%) ÷ 100 | Loss% = (CP − SP) ÷ CP × 100

⇒ Let the Cost Price (CP) be 100.

⇒ Marked Price (MP) = 100 + 5% of 100 = 105.

⇒ Selling Price (SP) = 105 − 40% of 105 = 105 − 42 = 63.

⇒ Loss = CP − SP = 100 − 63 = 37.

⇒ Loss percentage = (37 ÷ 100) × 100 = 37%.

∴ The correct answer is 37%.

Additional Information

Marked Price & Discount

Discount is always calculated on the Marked Price. SP = MP × (100 − Discount%) ÷ 100.

Successive Percentage Change

When a value is increased by x% and then decreased by y%, the net effect is [x − y − (xy ÷ 100)]%.

Shortcut Trick

Net filling efficiency = (1/7 − 1/14) of tank per minute.

Net efficiency = (2 − 1)/14 = 1/14 of tank per minute.

Time to fill full tank = 14 minutes.

Time to fill one-half of the tank = 14 ÷ 2 = 7 minutes.

∴ The correct answer is 7 minutes.

Alternate Method

Given: Filling Pipe (A) = 7 minutes, Emptying Pipe (B) = 14 minutes.

Formula Used: Total Work = LCM of time taken; Efficiency = Work ÷ Time.

⇒ Combined Efficiency (A + B) = +2 − 1 = 1 unit/min.

⇒ Target Work = 1/2 × Total Capacity = 1/2 × 14 = 7 units.

⇒ Time required = Target Work ÷ Combined Efficiency = 7 ÷ 1 = 7 minutes.

∴ The correct answer is 7 minutes.

Additional Information

Pipes and Cisterns Rule

If an inlet pipe fills in x hours and an outlet pipe empties in y hours, net work done in 1 hour = (1/x − 1/y) when both are open.

Efficiency Concept

Filling efficiency is taken as positive (+), while emptying efficiency is always taken as negative (−).

Shortcut Trick

Ratio of Person to Sibling = 3 : 1

Sum of ratio parts = 3 + 1 = 4 units

4 units = 40 years → 1 unit = 10 years

Age of the person = 3 units = 3 × 10 = 30 years

∴ The correct answer is 30 years.

Alternate Method

Given:

Sum of ages = 40 years

Person age = 3 × Sibling age

Calculations:

⇒ Let the age of the sibling be x years.

⇒ Age of the person = 3x years.

⇒ x + 3x = 40

⇒ 4x = 40

⇒ x = 40 ÷ 4 = 10 years

⇒ Person age = 3 × 10 = 30 years.

∴ The correct answer is 30 years.

Additional Information

Ratio and Proportion in Ages

When ages are given in a ratio a:b and their sum is S, the ages are [a/(a+b)] × S and [b/(a+b)] × S.

Age Difference Constant

The difference between the ages of two people remains constant throughout their lives, regardless of how many years pass.

Future and Past Ages

If current age is x, then age 'n' years ago was (x − n) and age 'n' years later will be (x + n).

Shortcut Trick

Relative Speed (opposite direction) = 40 + 60 = 100 km/h.

Convert Speed to m/s: 100 × (5/18) = 250/9 m/s.

Total Distance to cover = Length of Train 1 + Length of Train 2 = 125 + 125 = 250 m.

Time = Distance ÷ Speed = 250 ÷ (250/9) = 9 seconds.

∴ The correct answer is 9 sec.

Alternate Method

Given: Speed of Train A (S₁) = 40 km/h, Speed of Train B (S₂) = 60 km/h, Length of each train (L) = 125 m.

Formula Used: Time = (L₁ + L₂) ÷ (S₁ + S₂)

⇒ Total Distance = 125 + 125 = 250 m

⇒ Relative Speed = 40 + 60 = 100 km/h

⇒ Relative Speed in m/s = 100 × (5/18) = 500/18 = 250/9 m/s

⇒ Time taken = 250 ÷ (250/9)

⇒ Time taken = 250 × (9/250) = 9 seconds

∴ The correct answer is 9 sec.

Additional Information

Relative Speed Concept

When two objects move in opposite directions, relative speed is the sum of individual speeds (S₁ + S₂). If moving in the same direction, it is the difference (S₁ − S₂).

Unit Conversion

To convert speed from km/h to m/s, multiply by 5/18. To convert from m/s to km/h, multiply by 18/5.

Crossing Distance

When a train crosses another train, platform, or bridge, the total distance is always the sum of their lengths.

Shortcut Trick

Convert terms to the same prime base: 125 = 5³ and 0.25 = 1/4

⇒ 5^1/4 × (5³)^1/4

⇒ 5^1/4 × 5^3/4 = 5^{(1/4 + 3/4)}

⇒ 5¹ = 5

∴ The correct answer is 5.

Alternate Method

Given:

Expression = 5^1/4 × 125^0.25

Formula Used:

a^m × b^m = (a × b)^m

Calculation:

⇒ Since 1/4 = 0.25, the expression can be written as:

⇒ 5^0.25 × 125^0.25

⇒ Applying the formula a^m × b^m = (a × b)^m:

⇒ (5 × 125)^0.25

⇒ 625^0.25

⇒ Converting the decimal power back to a fraction (0.25 = 1/4):

⇒ 625^1/4

⇒ We know that 625 = 5 × 5 × 5 × 5 = 5⁴

⇒ (5⁴)^1/4

⇒ 5^{4 × (1/4)}

⇒ 5¹ = 5

∴ The correct answer is 5.

Additional Information

Product Rule of Indices

When multiplying terms with the same base, add their exponents: a^m × aⁿ = a^m+n

Power of a Power Rule

When raising a power to another power, multiply the exponents: (a^m)ⁿ = a^mn

Power of a Product Rule

When multiplying terms with the same exponent, multiply their bases: a^m × b^m = (a × b)^m

Shortcut Trick

Winner votes = Total Votes × Valid % × Winner %

Winner votes = 2,00,000 × (100 − 18)% × 80%

Winner votes = 2,00,000 × 0.82 × 0.80 = 1,31,200

∴ The correct answer is 1,31,200 votes.

Alternate Method

Given:

Total Votes = 2,00,000

Invalid Votes = 18%

Winner Shares = 80% of Valid Votes

Calculations:

⇒ Total Valid Votes = Total Votes × (100% − 18%)

⇒ Total Valid Votes = 2,00,000 × 82/100 = 1,64,000

⇒ Votes for Winner = 80% of 1,64,000

⇒ Votes for Winner = (80/100) × 1,64,000

⇒ Votes for Winner = 0.8 × 1,64,000 = 1,31,200

∴ The correct answer is 1,31,200 votes.

Additional Information

Election Base Value

Always identify if percentages are of Total Votes or Valid Votes. Winner % + Loser % = 100% of Valid Votes.

Victory Margin

Victory Margin = (Winner % − Loser %) × Valid Votes. This is the difference in votes between the two candidates.

Successive Percentage

When multiple deductions occur (Invalid then Winner), the final value is A × (1 − r₁/100) × (r₂/100).

Shortcut Trick

Combined efficiency of A, B, and C with Total Work = 6 units:

Efficiency of A = 2, B = 1, C = 3 ⇒ Total Efficiency = 6

Twice the work = 2 × 6 = 12 units

Time taken = 12 ÷ 6 = 2 days

∴ The correct answer is 2 days.

Alternate Method

Given:

Time taken by A = 3 days

Time taken by B = 6 days

Time taken by C = 2 days

Formula Used:

Total Work = LCM of individual times

Efficiency = Total Work ÷ Time Taken

Time Taken = Total Work ÷ Combined Efficiency

Calculations:

⇒ Total Efficiency of (A + B + C) = 2 + 1 + 3 = 6 units/day

⇒ New Total Work = 2 × 6 = 12 units

⇒ Required Time = 12 ÷ 6 = 2 days

∴ The correct answer is 2 days.

Additional Information

LCM Method for Time & Work

Using the LCM of individual days as the total work unit simplifies complex calculations into basic integer addition and division.

Work and Efficiency Relation

Work is directly proportional to efficiency when time is constant, and inversely proportional to time when work is constant (Work = Efficiency × Time).

Shortcut Trick

When distance is constant, speed is inversely proportional to time.

Ratio of Normal Speed to New Speed = 4 : 3

Ratio of Normal Time to New Time = 3 : 4

Difference in time units = 4 − 3 = 1 unit → 30 minutes

Usual Time = 3 units = 3 × 30 = 90 minutes.

∴ The correct answer is 90 min.

Alternate Method

Given: New Speed = 3/4 of Normal Speed, Time Delay = 30 minutes.

Formula Used: Speed × Time = Distance | Time = Distance ÷ Speed

⇒ Let normal speed be S and normal time be T.

⇒ Distance (D) = S × T

⇒ New Speed = 0.75S, New Time = T + 30

⇒ S × T = 0.75S × (T + 30)

⇒ T = 0.75T + 22.5

⇒ 0.25T = 22.5

⇒ T = 22.5 ÷ 0.25 = 90

∴ The correct answer is 90 min.

Additional Information

Inverse Variation Rule

When distance is constant, if speed becomes a/b of its original value, time becomes b/a of its original value.

Time Delay Formula

Usual Time = (Late Time × Numerator) ÷ (Denominator − Numerator) = (30 × 3) ÷ (4 − 3) = 90 minutes.

Average Speed

Average Speed for same distance covered at different speeds S₁ and S₂ is 2S₁S₂ ÷ (S₁ + S₂).

Shortcut Trick

Increase in Average = (New score − Old average) ÷ Total innings

⇒ Increase = (194 − 80) ÷ 6

⇒ Increase = 114 ÷ 6 = 19

∴ The correct answer is 19.

Alternate Method

Given: Average of 5 innings = 80 runs, 6^th inning score = 194 runs.

Formula: New Average = Total Runs ÷ Total Innings

⇒ Total runs in 5 innings = 5 × 80 = 400

⇒ Total runs in 6 innings = 400 + 194 = 594

⇒ New average = 594 ÷ 6 = 99

⇒ Increase in average = New average − Old average

⇒ Increase = 99 − 80 = 19

∴ The correct answer is 19.

Additional Information

Net Deviation Method

The sum of deviations of all observations from their average is always zero. The extra runs in the new inning are distributed equally among all innings to find the average increase.

Combined Average Formula

Combined Average = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂), where n is the number of items and x is the average of those items.

Excluded Value Effect

When a value is removed, if the average decreases, the excluded value was greater than the old average; if the average increases, the excluded value was smaller.

Shortcut Trick

For a 10% rate compounded annually for 2 years, the effective interest rate is calculated as: 10 + 10 + (10 × 10 / 100) = 21%.

The total Amount represents 100% (Principal) + 21% (Interest) = 121% of the Principal.

Amount = 7,300 × 121/100 = 73 × 121 = 8,833.

∴ The correct answer is ₹8,833.

Alternate Method

Given:

Principal (P) = ₹7,300

Rate (R) = 10% per annum

Time (T) = 2 years

Formula Used:

Amount (A) = P(1 + R/100)^T

Calculations:

⇒ A = 7300 × (1 + 10/100)²

⇒ A = 7300 × (1 + 1/10)²

⇒ A = 7300 × (11/10) × (11/10)

⇒ A = 7300 × 121 / 100

⇒ A = 73 × 121

⇒ A = 8833

∴ The correct answer is ₹8,833.

Additional Information

Effective Rate for Compound Interest

For a rate R% for 2 years, the effective interest rate is R + R + (R×R)/100.

Difference between CI and SI

For 2 years, the difference between Compound Interest and Simple Interest is P(R/100)².

Amount vs Interest

Interest is only the extra money earned, whereas Amount is the sum of the initial Principal and the interest earned.

Shortcut Trick

Initial Price = 100

Final Price = 100 × 0.90 × 0.55 × 0.45 × 1.55

Final Price = 34.52925

Net Change = 100 − 34.52925 = 65.47075%

∴ The correct answer is Decreases by 65.47%.

Alternate Method

Given: Successive changes of −10%, −45%, −55%, and +55%.

Formula: Final Price = Initial Price × (1 ± r₁/100) × (1 ± r₂/100) ...

⇒ Let original price be 100.

⇒ Price after 1^st month = 100 × (1 − 10/100) = 90

⇒ Price after 2^nd month = 90 × (1 − 45/100) = 90 × 0.55 = 49.5

⇒ Price after 3^rd month = 49.5 × (1 − 55/100) = 49.5 × 0.45 = 22.275

⇒ Price after 4^th month = 22.275 × (1 + 55/100) = 22.275 × 1.55 = 34.52625

⇒ Percentage change = ((34.52625 − 100) ÷ 100) × 100 = −65.47375%

⇒ Rounding to two decimal places, we get 65.47% decrease.

∴ The correct answer is Decreases by 65.47%.

Additional Information

Successive Percentage Change

For two successive changes a% and b%, the net effective change is given by (a + b + ab/100)%.

Multiplying Factor Method

To find the final value after multiple changes, multiply the initial value by (1 + r/100) for increase and (1 − r/100) for decrease.

Percentage Increase/Decrease

Percentage change = [(Final Value − Initial Value) ÷ Initial Value] × 100. Positive result denotes increase, negative denotes decrease.

Shortcut Trick

Identify the minimum difference between any two numbers: 5440 − 4220 = 1220 and 6880 − 5440 = 1440.

The HCF must be a factor of the difference 1220.

Check the options: 1220 is not divisible by 80, 60, or 40.

1220 ÷ 20 = 61. Since 20 divides all three numbers, it is the HCF.

∴ The correct answer is 20.

Alternate Method

Given: Numbers are 4220, 5440, and 6880.

Formula Used: HCF (Highest Common Factor) is the greatest number that divides each of the numbers without a remainder.

Using Long Division Method for 4220 and 5440:

⇒ 5440 = 4220 × 1 + 1220

⇒ 4220 = 1220 × 3 + 560

⇒ 1220 = 560 × 2 + 100

⇒ 560 = 100 × 5 + 60

⇒ 100 = 60 × 1 + 40

⇒ 60 = 40 × 1 + 20

⇒ 40 = 20 × 2 + 0

⇒ HCF of 4220 and 5440 is 20.

Now, check if 6880 is divisible by 20:

⇒ 6880 ÷ 20 = 344 (Exactly divisible)

∴ The correct answer is 20.

Additional Information

Properties of HCF

The HCF of two or more numbers is the greatest divisor that divides them exactly. HCF is always less than or equal to the smallest number.

Relation between HCF and LCM

For two numbers a and b: HCF × LCM = a × b. This property is widely used to find one value if the others are known.

HCF of Fractions

HCF of Fractions = (HCF of Numerators) ÷ (LCM of Denominators).

Shortcut Trick

Assume all 15 coins are ₹10 coins: Total value = 15 × 10 = ₹150.

Difference from actual value = 150 − 85 = ₹65.

Difference between coin denominations = 10 − 5 = ₹5.

Number of ₹5 coins = Total Difference ÷ Denomination Difference = 65 ÷ 5 = 13.

∴ The correct answer is 13 coins.

Alternate Method

Given:

Total coins = 15

Total value = ₹85

Let the number of ₹5 coins be x.

Then the number of ₹10 coins = (15 − x).

Calculation:

⇒ 10 × (15 − x) + 5 × x = 85

⇒ 150 − 10x + 5x = 85

⇒ 150 − 5x = 85

⇒ 5x = 150 − 85

⇒ 5x = 65

⇒ x = 65 ÷ 5

⇒ x = 13

∴ The correct answer is 13 coins.

Additional Information

Linear Equation in One Variable

An equation which can be written in the form ax + b = 0, where a and b are real numbers and a ≠ 0.

Alligation Method

Average value per coin = 85 ÷ 15 = ₹17/3. Ratio of (₹10 coins) to (₹5 coins) = (17/3 − 5) : (10 − 17/3) = 2/3 : 13/3 = 2 : 13.

Shortcut Trick

Apply the inverse proportion formula: M₁ × D₁ = M₂ × D₂

Here, 46 × 13 = 27 × Time

⇒ Time = 598 ÷ 27

⇒ Time ≈ 22.15 minutes

∴ The correct answer is 22.15 minutes.

Alternate Method

Given:

Number of initial pipes (n₁) = 46

Time taken initially (t₁) = 13 minutes

Number of final pipes (n₂) = 27

Formula Used:

Since the capacity of the tank is constant, the time taken is inversely proportional to the number of pipes used.

Total Work = Pipes × Time

Calculations:

⇒ Total Work = 46 × 13 = 598 units

⇒ Time required for 27 pipes = Total Work ÷ n₂

⇒ Time = 598 ÷ 27

⇒ Time = 22.148148...

⇒ Time ≈ 22.15 minutes (rounded to two decimal places)

∴ The correct answer is 22.15 minutes.

Additional Information

Inverse Proportion

When one quantity increases while the other decreases proportionally, they are in inverse proportion. Formula: x₁y₁ = x₂y₂.

Pipes and Cisterns Logic

Efficiency of multiple identical pipes is additive. Total volume = (Number of pipes) × (Efficiency of one pipe) × (Time taken).

Shortcut Trick

Radius (r) = 5 cm and Height (h) = 35 cm.

Curved Surface Area (CSA) = 2 × (22/7) × 5 × 35 = 1100 cm².

Total Cost = 1100 × 12 = ₹13,200.

Net Paid Amount (after 10% discount) = 13,200 × 0.9 = ₹11,880.

∴ The correct answer is ₹11,880.

Alternate Method

Given:

Diameter of the cylindrical pillar = 10 cm ⇒ Radius (r) = 10/2 = 5 cm.

Height (h) = 35 cm.

Painting Rate = ₹12/cm².

Discount = 10%.

Formula Used:

Curved Surface Area (CSA) = 2πrh

Net Amount = Total Cost − Discount

Calculations:

⇒ Curved Surface Area = 2 × (22/7) × 5 × 35

⇒ Curved Surface Area = 2 × 22 × 5 × 5

⇒ Curved Surface Area = 1100 cm²

⇒ Total Painting Cost = 1100 × 12 = ₹13,200

⇒ Discount Amount = 10% of 13,200 = (10/100) × 13200 = ₹1,320

⇒ Final Amount Paid = 13,200 − 1,320 = ₹11,880

∴ The correct answer is ₹11,880.

Additional Information

Total Surface Area of a Cylinder

The Total Surface Area (TSA) includes both the curved surface and the two circular bases: TSA = 2πrh + 2πr² = 2πr(h + r).

Volume of a Cylinder

The Volume represents the capacity of the cylinder: Volume = πr²h.

Successive Discount Formula

If two successive discounts x% and y% are given, the single equivalent discount is [x + y − (xy/100)]%.

Shortcut Trick

New Income = 50,000 × 1.1 = ₹55,000

Saving % = 100% − 40% = 60%

New Saving = 60% of 55,000 = 0.60 × 55,000

New Saving = ₹33,000

∴ The correct answer is ₹33,000.

Alternate Method

Given:

Initial Income = ₹50,000

Expenditure Rate = 40%

Income Increment = 10%

Calculations:

⇒ New Income = 50,000 + (10/100 × 50,000)

⇒ New Income = 50,000 + 5,000 = ₹55,000

⇒ New Expenditure = 40% of 55,000

⇒ New Expenditure = 0.40 × 55,000 = ₹22,000

⇒ New Savings = New Income − New Expenditure

⇒ New Savings = 55,000 − 22,000 = ₹33,000

∴ The correct answer is ₹33,000.

Additional Information

Percentage Change in Savings

If both income and expenditure increase by the same percentage (k%), then savings also increase by exactly k%.

Income-Expenditure Formula

Income = Expenditure + Savings. This base identity is used to solve all budget and personal finance aptitude problems.

Successive Percentage

When a value is increased by x% and then y%, the net effective change is (x + y + xy/100)%.

Shortcut Trick

Total Cost Price (CP) of 20 pens = ₹200.

Selling Price (SP) of 1 pen = ₹12.

Total Selling Price (SP) = 20 × 12 = ₹240.

Total Profit = Total SP − Total CP = 240 − 200 = ₹40.

∴ The correct answer is ₹40.

Alternate Method

Given: Total CP = ₹200, Number of pens = 20, SP per pen = ₹12.

Formulas: Profit = SP − CP | CP per unit = Total CP ÷ Quantity.

⇒ Cost Price of one pen = 200 ÷ 20 = ₹10.

⇒ Profit per pen = SP per pen − CP per pen = 12 − 10 = ₹2.

⇒ Total Profit = Profit per pen × Total pens = 2 × 20 = ₹40.

∴ The correct answer is ₹40.

Additional Information

Profit and Loss Percentage

Profit% is always calculated on the Cost Price (CP). Formula: Profit% = (Profit ÷ CP) × 100.

Selling Price Calculation

If profit percentage is given: SP = CP × (100 + Profit%) ÷ 100.

Shortcut Trick

Combine ratios A : B = 20 : 2 (or 10 : 1) and B : C = 1 : 4.

Combined ratio A : B : C = 10 : 1 : 4.

Total units = 10 + 1 + 4 = 15 units.

Share of B = (1 ÷ 15) × 13,800 = 920.

∴ The correct answer is ₹920.

Alternate Method

Given:

Total Profit = ₹13,800

Ratio A : B = 20 : 2 = 10 : 1

Ratio B : C = 1 : 4

Calculations:

⇒ Common ratio A : B : C = 10 : 1 : 4

⇒ Let shares be 10x, 1x, and 4x

⇒ 10x + 1x + 4x = 13,800

⇒ 15x = 13,800

⇒ x = 13,800 ÷ 15

⇒ x = 920

⇒ Share of B = 1x = ₹920

∴ The correct answer is ₹920.

Additional Information

Compound Ratio

To combine A : B and B : C, make the value of B common in both ratios by multiplying with suitable factors.

Partnership Profit Distribution

Profit is distributed in the ratio of (Capital × Time). If time is same, profit ratio equals the investment ratio.

Ratio to Value Conversion

Individual share = (Individual ratio part ÷ Total ratio parts) × Total value.

Shortcut Trick

Age of new person = New Average + (Initial number of members × Increase in average)

Given: New Average = 42 years, Initial members = 23 students, Increase = 1 year (42 − 41)

⇒ Teacher's Age = 42 + (23 × 1)

⇒ Teacher's Age = 42 + 23 = 65 years.

∴ The correct answer is 65 years.

Alternate Method

Given:

Initial number of students = 23

Initial average age = 41 years

New number of members (including teacher) = 24

New average age = 42 years

Formula Used:

Total Age = Average × Number of persons

Age of added person = (New Total Age) − (Initial Total Age)

Calculations:

⇒ Total age of 23 students = 23 × 41

⇒ Total age of 23 students = 943 years

⇒ Total age of 24 persons (students + teacher) = 24 × 42

⇒ Total age of 24 persons = 1008 years

⇒ Age of the teacher = 1008 − 943

⇒ Age of the teacher = 65 years

∴ The correct answer is 65 years.

Additional Information

Average Concept

Average = (Sum of all observations) ÷ (Total number of observations). It represents the central value of a data set.

Excluded Observation

If a person leaves the group, the age of the person = (Old Average × Old Count) − (New Average × New Count).

Effect of Replacement

If one person is replaced by another: Age of New Person = Age of Old Person + (Total count × Change in average).