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Question 241

RRB NTPC 2026β€’ Mathematicsβ€’ Mathematics

The arithmetic mean of 25 observations is 32.6. If the arithmetic mean of the first 24 observations is 30, what is the 25th observation?

  1. AOption (a)

    90

  2. BOption (b)

    80

  3. COption (c)

    95

  4. DOption (d)

    85

View answer & explanation

Correct answer

Answer: (c)C.

95

Why this answer is correct

Shortcut Trick

Use the Deviation Method: The 25th observation accounts for the total change in the mean.

Change in Mean = 32.6 βˆ’ 30 = 2.6

Total Deviation = 24 Γ— 2.6 = 62.4

25th observation = New Mean + Total Deviation = 32.6 + 62.4 = 95

∴ The correct answer is 95.

Alternate Method

Given:

Arithmetic Mean of 25 observations = 32.6

Arithmetic Mean of the first 24 observations = 30

Formula Used:

Sum of observations = Mean Γ— Total Number of observations

Calculations:

β‡’ Total sum of 25 observations = 25 Γ— 32.6 = 815

β‡’ Total sum of first 24 observations = 24 Γ— 30 = 720

β‡’ 25th observation = Total Sum (25) βˆ’ Total Sum (24)

β‡’ 25th observation = 815 βˆ’ 720 = 95

∴ The correct answer is 95.

Additional Information

Arithmetic Mean Formula

The average or Mean (xΒ―) is calculated as the sum of all values divided by the total number of values: xΒ― = (βˆ‘xi) Γ· n.

Effect of Inclusion/Exclusion

When a new value is added, the New Sum = (Old Average Γ— Old Count) + New Value. Conversely, New Value = (New Average Γ— New Count) βˆ’ (Old Average Γ— Old Count).

Deviation Concept

The sum of deviations of all observations from their arithmetic mean is always zero (βˆ‘(xi βˆ’ xΒ―) = 0).

Question 242

RRB NTPC 2026β€’ Mathematicsβ€’ Mathematics

A dishonest shopkeeper professes to sell his goods at a 35% loss but uses a false balance and gains 85%. The actual weight (rounded off to one decimal place) he uses for 1 kg is:

  1. AOption (a)

    347.2 gm

  2. BOption (b)

    348.5 gm

  3. COption (c)

    351.4 gm

  4. DOption (d)

    349.4 gm

View answer & explanation

Correct answer

Answer: (c)C.

351.4 gm

Why this answer is correct

Shortcut Trick

Use the Effective Multiplier logic: Total Gain Factor = Price Factor Γ— Weight Factor.

Total Gain 85% β†’ Factor = 1.85 | Loss 35% β†’ Factor = 0.65.

Weight Factor = 1000 / Actual Weight (x).

1.85 = 0.65 Γ— (1000 / x) β‡’ x = 650 / 1.85.

x = 351.35... β‰ˆ 351.4 gm.

∴ The correct answer is 351.4 gm.

Alternate Method

Given: Professed Loss = 35%, Overall Gain = 85%, Standard weight = 1000 gm.

Let the Actual Weight used by the shopkeeper be x gm.

Let the Cost Price (CP) of 1 gm be β‚Ή1.

β‡’ CP of 1000 gm = β‚Ή1000.

β‡’ Selling Price (SP) at 35% loss = 1000 βˆ’ (35% of 1000) = β‚Ή650.

β‡’ The shopkeeper actually gives x gm for β‚Ή650.

β‡’ Actual CP of x gm = β‚Ήx.

β‡’ Overall Gain% = [(SP βˆ’ CP) / CP] Γ— 100

β‡’ 85 = [(650 βˆ’ x) / x] Γ— 100

β‡’ 0.85 = (650 / x) βˆ’ 1

β‡’ 1.85 = 650 / x

β‡’ x = 650 / 1.85 = 351.351...

β‡’ x β‰ˆ 351.4 gm (rounded to one decimal place).

∴ The correct answer is 351.4 gm.

Additional Information

Dishonest Dealer Formula

Profit % = [(True Weight βˆ’ False Weight) / False Weight] Γ— 100, assuming goods are sold at cost price.

Overall Profit with Price Change

Final Gain/Loss % = [((100 Β± P/L%) / 100) Γ— (True Weight / False Weight) βˆ’ 1] Γ— 100.

Multiplier Method

Effective Multiplier (Mtotal) = Mprice Γ— Mweight. If M > 1, it is a profit; if M < 1, it is a loss.

Question 243

RRB NTPC 2026β€’ Mathematicsβ€’ Mathematics

Add 1116 \frac{11}{16} and 0.4375. What is the sum in decimal form?

  1. AOption (a)

    1.208

  2. BOption (b)

    1.125

  3. COption (c)

    0.975

  4. DOption (d)

    0.958

View answer & explanation

Correct answer

Answer: (b)B.

1.125

Why this answer is correct

Shortcut Trick

Convert the fraction 11/16 into its decimal equivalent: 11 Γ· 16 = 0.6875.

Perform the addition with the given decimal: 0.6875 + 0.4375 = 1.125.

∴ The correct answer is 1.125.

Alternate Method

Given:

Fraction = 11/16

Decimal = 0.4375

Formula Used:

Decimal to Fraction conversion: Value / 10n (where n is the number of decimal places).

Calculations:

β‡’ Convert 0.4375 to a fraction: 0.4375 = 4375 Γ· 10000

β‡’ Simplify the fraction: 4375/10000 = 875/2000 = 175/400 = 35/80 = 7/16

β‡’ Calculate the Sum: 11/16 + 7/16 = (11 + 7) Γ· 16

β‡’ Sum = 18/16 = 9/8

β‡’ Convert 9/8 to decimal form: 9 Γ· 8 = 1.125

∴ The correct answer is 1.125.

Additional Information

Fraction to Decimal Conversion

A fraction is converted to a decimal by dividing the numerator by the denominator. If the denominator is in the form 2m Γ— 5n, the decimal will be terminating.

Adding Decimals

To add decimals, align the decimal points and add as whole numbers, then place the decimal point directly below the others in the sum.

Like Fractions

Fractions with the same denominator are called like fractions. Their addition or subtraction is done by performing the operation on the numerators while keeping the denominator constant.

Question 244

RRB NTPC 2026β€’ Mathematicsβ€’ Mathematics

A sum of β‚Ή2000 is invested at 20% compound interest per annum, compounded annually for 2 years. What is the compound interest earned at the end of 2 years?

  1. AOption (a)

    β‚Ή1000

  2. BOption (b)

    β‚Ή900

  3. COption (c)

    β‚Ή800

  4. DOption (d)

    β‚Ή880

View answer & explanation

Correct answer

Answer: (d)D.

β‚Ή880

Why this answer is correct

Shortcut Trick

Effective Rate of Interest for 2 years = x + y + (xy/100)%

β‡’ 20 + 20 + (20 Γ— 20)/100 = 44%

Compound Interest (CI) = 44% of β‚Ή2000

β‡’ 0.44 Γ— 2000 = β‚Ή880

∴ The correct answer is β‚Ή880.

Alternate Method

Given: Principal (P) = β‚Ή2000, Rate (R) = 20%, Time (n) = 2 years

Formula Used: Amount (A) = P(1 + R/100)n

β‡’ A = 2000(1 + 20/100)2

β‡’ A = 2000(1.2)2

β‡’ A = 2000 Γ— 1.44 = β‚Ή2880

β‡’ Compound Interest = Amount βˆ’ Principal

β‡’ CI = 2880 βˆ’ 2000 = β‚Ή880

∴ The correct answer is β‚Ή880.

Additional Information

Difference between CI and SI

For a period of 2 years, the difference (D) between Compound Interest and Simple Interest is given by D = P Γ— (R/100)2.

Effective Rate Formula

To find the equivalent single percentage for two successive increases of x% and y%, use the formula: x + y + (xy/100)%.

Compound Interest Ratio Method

For 2 years, the ratio 2:1 can be used. CI = 2 Γ— (Interest on P) + 1 Γ— (Interest on Interest).

Question 245

RRB NTPC 2026β€’ Mathematicsβ€’ Mathematics

The price of fuel decreases by 55%, 35% and 45% in three successive months, but increases by 40% in the fourth month. What is the percentage decrease in the price of fuel in the fourth month as compared to its original price? (Round off to 2 decimal places.)

  1. AOption (a)

    81.67%

  2. BOption (b)

    77.48%

  3. COption (c)

    76.52%

  4. DOption (d)

    73.05%

View answer & explanation

Correct answer

Answer: (b)B.

77.48%

Why this answer is correct

Shortcut Trick

Use the Successive Multiplier Method to find the final price ratio.

Final Price Factor = 0.45 Γ— 0.65 Γ— 0.55 Γ— 1.4 = 0.225225

Net Percentage Decrease = (1 βˆ’ 0.225225) Γ— 100 = 77.4775%

Rounding to 2 decimal places, we get 77.48%.

∴ The correct answer is 77.48%.

Alternate Method

Given: Successive decreases of 55%, 35%, 45% and an increase of 40%.

Formula Used: Final Price = Initial Price Γ— (1 Β± r1/100) Γ— (1 Β± r2/100) ...

Let the original price be 100.

β‡’ Price after 1st month = 100 βˆ’ 55% of 100 = 45

β‡’ Price after 2nd month = 45 βˆ’ 35% of 45 = 45 Γ— 0.65 = 29.25

β‡’ Price after 3rd month = 29.25 βˆ’ 45% of 29.25 = 29.25 Γ— 0.55 = 16.0875

β‡’ Price after 4th month = 16.0875 + 40% of 16.0875 = 16.0875 Γ— 1.4 = 22.5225

β‡’ Total decrease from original = 100 βˆ’ 22.5225 = 77.4775

β‡’ Percentage decrease = (77.4775 / 100) Γ— 100 = 77.4775%

∴ The correct answer is 77.48%.

Additional Information

Successive Percentage Change

When a value changes by a% and then by b%, the net change is [a + b + (ab/100)]%. For decreases, use negative values.

Multiplier Method

For a decrease of x%, the multiplier is (100 βˆ’ x)/100. For an increase of y%, it is (100 + y)/100. Multiply all factors to get the final ratio.

Rounding Rule

When rounding to 2 decimal places, check the 3rd decimal. If it is 5 or greater, round up the 2nd decimal.

Question 246

RRB NTPC 2026β€’ Mathematicsβ€’ Mathematics

If the height at which a ladder touches the wall is the mean proportional between 6 meters and 24 meters, at what height does the ladder touch the wall?

  1. AOption (a)

    18 meters

  2. BOption (b)

    14 meters

  3. COption (c)

    16 meters

  4. DOption (d)

    12 meters

View answer & explanation

Correct answer

Answer: (d)D.

12 meters

Why this answer is correct

Shortcut Trick

The mean proportional between two numbers a and b is calculated as √(a Γ— b).

Given a = 6 m and b = 24 m.

Height (h) = √(6 Γ— 24) = √144 = 12 m.

∴ The correct answer is 12 m.

Alternate Method

Given:

First value (a) = 6 m

Second value (b) = 24 m

The height (h) of the ladder on the wall is the mean proportional.

Formula Used:

If h is the mean proportional between a and b, then:

a : h = h : b β‡’ h2 = a Γ— b β‡’ h = √(a Γ— b)

Calculations:

β‡’ h = √(6 Γ— 24)

β‡’ h = √144

β‡’ h = 12 m

∴ The correct answer is 12 m.

Additional Information

Mean Proportional (Geometric Mean)

The mean proportional between two numbers a and b is the value x such that a/x = x/b, which gives x = √(ab).

Third Proportional

If a and b are two numbers, then their third proportional c is such that a/b = b/c, which gives c = b2/a.

Fourth Proportional

If a, b, and c are three numbers, then their fourth proportional d is such that a/b = c/d, which gives d = (b Γ— c)/a.

Question 247

RRB NTPC 2026β€’ Mathematicsβ€’ Mathematics

What sum (in β‚Ή) will earn a simple interest of β‚Ή1,440 in 2 years at 12% per year rate of interest?

  1. AOption (a)

    3,000

  2. BOption (b)

    12,000

  3. COption (c)

    6,000

  4. DOption (d)

    345.6

View answer & explanation

Correct answer

Answer: (c)C.

6,000

Why this answer is correct

Shortcut Trick

Effective Simple Interest rate for 2 years = 12% Γ— 2 = 24%.

According to the question, 24% of the Principal = β‚Ή1,440.

1% of the Principal = 1440 Γ· 24 = 60.

Total Principal (100%) = 60 Γ— 100 = β‚Ή6,000.

∴ The correct answer is β‚Ή6,000.

Alternate Method

Given:

Simple Interest (SI) = β‚Ή1,440

Rate of Interest (R) = 12% per annum

Time Period (T) = 2 years

Formula Used:

Simple Interest (SI) = (Principal Γ— Rate Γ— Time) Γ· 100

Calculations:

β‡’ 1440 = (P Γ— 12 Γ— 2) Γ· 100

β‡’ 1440 = (P Γ— 24) Γ· 100

β‡’ 1440 Γ— 100 = 24P

β‡’ P = 144000 Γ· 24

β‡’ P = 6000

∴ The correct answer is β‚Ή6,000.

Additional Information

Simple Interest (S.I.)

The interest remains constant every year as it is calculated only on the original principal. S.I. = (P Γ— R Γ— T) Γ· 100.

Amount (A)

Total sum of money (Principal + Interest) to be paid back at the end of the time period. A = P + S.I. = P[1 + (RT Γ· 100)].

Difference between C.I. and S.I.

For a period of 2 years, the difference is given by D = P Γ— (R Γ· 100)2.

Rate and Time Calculation

Rate R = (SI Γ— 100) Γ· (P Γ— T) and Time T = (SI Γ— 100) Γ· (P Γ— R).

Question 248

RRB NTPC 2026β€’ Mathematicsβ€’ Mathematics

A regular octagonal fountain has a circumradius of 10 m. Find the approximate length of each side.

  1. AOption (a)

    9.27 m

  2. BOption (b)

    6.13 m

  3. COption (c)

    7.65 m

  4. DOption (d)

    8.71 m

View answer & explanation

Correct answer

Answer: (c)C.

7.65 m

Why this answer is correct

Shortcut Trick

For a regular octagon with circumradius R, the side length a is given by:

a = 2 Γ— R Γ— sin(180Β° / 8) = 2 Γ— R Γ— sin(22.5Β°)

Given: R = 10 m and sin(22.5Β°) β‰ˆ 0.3827

a = 2 Γ— 10 Γ— 0.3827 β‡’ 20 Γ— 0.3827

a = 7.654 m β‰ˆ 7.65 m

∴ The correct answer is 7.65 m.

Alternate Method

Given: Circumradius (R) = 10 m, Number of sides (n) = 8.

Formula used: Law of Cosines in the triangle formed by the center and two adjacent vertices.

The central angle subtended by each side of the regular octagon at the center O is:

ΞΈ = 360Β° Γ· n β‡’ 360Β° Γ· 8 = 45Β°

In Ξ”OAB, let side AB = a, and OA = OB = R = 10 m.

Using Law of Cosines:

β‡’ a2 = R2 + R2 βˆ’ 2 Γ— R Γ— R Γ— cos(45Β°)

β‡’ a2 = 2R2 βˆ’ 2R2 Γ— (1/√2)

β‡’ a2 = 2R2 (1 βˆ’ 1/√2)

β‡’ a2 = 2 Γ— 102 Γ— (1 βˆ’ 0.7071)

β‡’ a2 = 200 Γ— 0.2929

β‡’ a2 = 58.58

β‡’ a = √58.58 β‰ˆ 7.6537 m

∴ The correct answer is 7.65 m.

Additional Information

Area of a Regular Octagon

The area can be calculated as Area = 2(1 + √2)a2, where a is the side length.

Interior and Exterior Angles

For a regular octagon, each exterior angle is 45Β° and each interior angle is 135Β°.

Inradius of a Regular Polygon

The distance from the center to the midpoint of a side is r = R Γ— cos(180Β°/n).

Question 249

RRB NTPC 2026β€’ Mathematicsβ€’ Mathematics

A bus travels at a uniform speed of 54 km/hr. How many meters does it cover in 1 minute?

  1. AOption (a)

    750 meters

  2. BOption (b)

    600 meters

  3. COption (c)

    800 meters

  4. DOption (d)

    900 meters

View answer & explanation

Correct answer

Answer: (d)D.

900 meters

Why this answer is correct

Shortcut Trick

Convert speed from km/hr to m/min directly.

Speed = 54 Γ— (1000 Γ· 60) m/min

Speed = 54 Γ— (50 Γ· 3) = 18 Γ— 50 = 900 m/min

In 1 minute, the bus covers 900 meters.

∴ The correct answer is 900 m.

Alternate Method

Given:

Speed of the bus = 54 km/hr

Time taken = 1 min

Formula Used:

Distance = Speed Γ— Time

Calculations:

β‡’ 1 km = 1000 m and 1 hr = 60 min

β‡’ Speed in m/min = (54 Γ— 1000) Γ· 60

β‡’ Speed = 54000 Γ· 60 = 900 m/min

β‡’ Distance = 900 m/min Γ— 1 min

β‡’ Distance = 900 m

∴ The correct answer is 900 m.

Additional Information

Unit Conversion Trick

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

Distance Formula

Distance = Speed Γ— Time. Always ensure that the units of speed and time are consistent (e.g., both in seconds or both in hours) before calculation.

Uniform Speed

When an object covers equal distances in equal intervals of time, it is said to be moving with uniform speed.

Question 250

RRB NTPC 2026β€’ Mathematicsβ€’ Mathematics

A motorist travels a certain journey in two stages. In the first stage, he travels for one-third of the total time at 30 km/hr. In the second stage, he travels for the rest of the time at 60 km/hr. He returns to the start at a uniform speed of 75 km/hr. What is the average speed for the entire round trip?

  1. AOption (a)

    55 km/hr

  2. BOption (b)

    60 km/hr

  3. COption (c)

    62 km/hr

  4. DOption (d)

    58 km/hr

View answer & explanation

Correct answer

Answer: (b)B.

60 km/hr

Why this answer is correct

Shortcut Trick

The average speed for the onward journey is the weighted average of speeds with respect to time.

Onward Average Speed = (1/3 Γ— 30) + (2/3 Γ— 60) = 10 + 40 = 50 km/hr.

Since the distance for the onward journey and return journey is equal, use the harmonic mean formula:

Average Speed = (2 Γ— Von Γ— Vret) Γ· (Von + Vret) = (2 Γ— 50 Γ— 75) Γ· (50 + 75) = 7500 Γ· 125 = 60 km/hr.

∴ The correct answer is 60 km/hr.

Alternate Method

Given:

Stage 1: Speed = 30 km/hr, Time = 1/3 of total onward time.

Stage 2: Speed = 60 km/hr, Time = 2/3 of total onward time.

Return Speed: 75 km/hr.

Calculations:

β‡’ Let the total time for the onward journey be 3 hours.

β‡’ Time for Stage 1 = 1/3 Γ— 3 = 1 hour.

β‡’ Time for Stage 2 = 2/3 Γ— 3 = 2 hours.

β‡’ Distance in Stage 1 = Speed Γ— Time = 30 Γ— 1 = 30 km.

β‡’ Distance in Stage 2 = Speed Γ— Time = 60 Γ— 2 = 120 km.

β‡’ Total onward distance = 30 + 120 = 150 km.

β‡’ Return journey distance = 150 km.

β‡’ Return time = Distance Γ· Speed = 150 Γ· 75 = 2 hours.

β‡’ Total Trip Distance = Onward + Return = 150 + 150 = 300 km.

β‡’ Total Trip Time = Onward Time + Return Time = 3 + 2 = 5 hours.

β‡’ Average speed = Total Distance Γ· Total Time = 300 Γ· 5 = 60 km/hr.

∴ The correct answer is 60 km/hr.

Additional Information

Average Speed (Equal Distance)

When two equal distances are covered at speeds V1 and V2, the average speed is 2V1V2 Γ· (V1 + V2).

Average Speed (Equal Time Intervals)

If a journey is divided into equal time intervals at different speeds, the average speed is the simple arithmetic mean: (V1 + V2 + ... + Vn) Γ· n.

General Average Speed Formula

Average Speed = Total Distance Γ· Total Time. This applies to all scenarios regardless of uniformity in time or distance.

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