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Question 751

SBI Clerk 2025• Numerical Ability

A train running at a speed of 20 m/s takes 22 seconds to pass a bridge and it takes 10 seconds to pass a man who is running at a speed of 5 m/s in the same direction. Find the length of the bridge.

  1. AOption (a)

    150 m

  2. BOption (b)

    200 m

  3. COption (c)

    290 m

  4. DOption (d)

    300 m

  5. EOption (e)

    350 m

View answer & explanation

Correct answer

Answer: (c)C.

290 m

Why this answer is correct

Shortcut Trick

Relative Speed with man = 20 − 5 = 15 m/s.

Length of Train (LT) = Relative Speed × Time = 15 × 10 = 150 m.

Total distance to cross bridge = LT + LB = Train Speed × Time = 20 × 22 = 440 m.

Length of Bridge (LB) = 440 − 150 = 290 m.

∴ The correct answer is 290 m.

Alternate Method

Given:

Speed of train (VT) = 20 m/s

Speed of man (VM) = 5 m/s (Same direction)

Time to pass man (t1) = 10 s

Time to pass bridge (t2) = 22 s

Formula Used:

Distance = Speed × Time

Relative Speed (Same direction) = V1 − V2

Calculations:

⇒ Relative speed of train w.r.t man = 20 − 5 = 15 m/s

⇒ Length of train (LT) = Relative Speed × t1 = 15 × 10 = 150 m

⇒ Total distance to cross bridge = LT + Length of Bridge (LB)

⇒ LT + LB = VT × t2

⇒ 150 + LB = 20 × 22

⇒ 150 + LB = 440

⇒ LB = 440 − 150 = 290 m

∴ The correct answer is 290 m.

Additional Information

Relative Speed

When two objects move in the same direction, relative speed = S1 − S2. In opposite directions, relative speed = S1 + S2.

Crossing Stationary Objects

To cross a point object (pole, man), distance = LTrain. To cross an object with length (bridge, platform), distance = LTrain + LObject.

Unit Conversion

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

Question 752

SBI Clerk 2025• Numerical Ability

A container contains 100 litres of milk. If 10 % of milk was replaced by water and this process was repeated two times more, then find the quantity of the milk in the final mixture.

  1. AOption (a)

    82.9 litres

  2. BOption (b)

    72.9 litres

  3. COption (c)

    62.9 litres

  4. DOption (d)

    72 litres

  5. EOption (e)

    None of these

View answer & explanation

Correct answer

Answer: (b)B.

72.9 litres

Why this answer is correct

Shortcut Trick

Initial quantity = 100 litres

Replacement fraction = 10% = 1/10

Remaining fraction after 1 process = 1 − 1/10 = 9/10

Since the process is repeated two times more (total 3 times):

Final Milk = 100 × (9/10)3 = 100 × 729/1000 = 72.9 litres

∴ The correct answer is 72.9 litres.

Alternate Method

Given:

Initial quantity of milk (x) = 100 litres

Quantity replaced (y) = 10% of 100 = 10 litres

Number of times the process is performed (n) = 3

Formula Used:

Final quantity = x × (1 − y/x)n

Calculations:

⇒ Final Quantity = 100 × (1 − 10/100)3

⇒ Final Quantity = 100 × (1 − 1/10)3

⇒ Final Quantity = 100 × (9/10) × (9/10) × (9/10)

⇒ Final Quantity = 100 × 0.9 × 0.9 × 0.9

⇒ Final Quantity = 100 × 0.729

⇒ Final Quantity = 72.9 litres

∴ The correct answer is 72.9 litres.

Additional Information

Successive Replacement Formula

The formula Final Quantity = Initial × (1 − r/100)n is used when a fixed percentage r is replaced n times.

Mixture Replacement with Different Quantities

If different amounts a, b, c are replaced each time, the final quantity is x × (1 − a/x) × (1 − b/x) × (1 − c/x).

Ratio of Milk to Water

After the process, the quantity of water = Total Capacity − Final Milk. In this case, 100 − 72.9 = 27.1 litres.

Question 753

SBI Clerk 2025• Numerical Ability

The average of 30 numbers is 9, the average of first 15 numbers is 8 and that of next 13 numbers is also 8. What will be the average of last two numbers?

  1. AOption (a)

    46

  2. BOption (b)

    20

  3. COption (c)

    23

  4. DOption (d)

    12

  5. EOption (e)

    9

View answer & explanation

Correct answer

Answer: (c)C.

23

Why this answer is correct

Shortcut Trick

Total deviation from average (9) for 28 numbers = 28 × (8 − 9) = −28.

To maintain the average, the last two numbers must compensate for this deficit.

Sum of last two numbers = (2 × 9) + 28 = 18 + 28 = 46.

Average of last two numbers = 46 ÷ 2 = 23.

∴ The correct answer is 23.

Alternate Method

Given: Total numbers = 30, Overall average = 9, First 15 average = 8, Next 13 average = 8.

⇒ Total sum of 30 numbers = 30 × 9 = 270

⇒ Sum of first 15 numbers = 15 × 8 = 120

⇒ Sum of next 13 numbers = 13 × 8 = 104

⇒ Sum of last 2 numbers = Total sum − (Sum of 15 + Sum of 13)

⇒ Sum of last 2 numbers = 270 − (120 + 104) = 270 − 224 = 46

⇒ Average of last 2 numbers = 46 ÷ 2 = 23

∴ The correct answer is 23.

Additional Information

Basic Average Formula

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

Net Deviation Method

The sum of deviations of all observations from the arithmetic mean is always zero. This helps in finding missing values quickly.

Weighted Average

When groups have different sizes, Combined Average = (n1x1 + n2x2 + ...) ÷ (n1 + n2 + ...).

Question 754

SBI Clerk 2025• Numerical Ability

A can complete a work in 12 days, B can complete the same work in 7(1/2) days, and B along with C together can complete the work in 7(1/5) days. How many days will C alone take to complete the work?

  1. AOption (a)

    100 days

  2. BOption (b)

    120 days

  3. COption (c)

    150 days

  4. DOption (d)

    180 days

  5. EOption (e)

    200 days

View answer & explanation

Correct answer

Answer: (d)D.

180 days

Why this answer is correct

Shortcut Trick

Convert mixed fractions: B = 15/2 days, B+C = 36/5 days.

Total Work (LCM of 12, 15, 36) = 180 units.

Efficiency: B = 180 ÷ (15/2) = 24; B + C = 180 ÷ (36/5) = 25.

Efficiency of C = (B + C) − B = 25 − 24 = 1 unit/day.

Time taken by C = 180 ÷ 1 = 180 days.

∴ The correct answer is 180 days.

Alternate Method

Given:

Time taken by A = 12 days

Time taken by B = 7(1/2) days = 15/2 days

Time taken by B + C = 7(1/5) days = 36/5 days

Formula Used:

Total Work = Time × Efficiency

Efficiency = Total Work ÷ Time

PersonDaysTotal WorkEfficiency
A1218015
B15/224
B + C36/525

Calculations:

⇒ Total work = LCM of numerators (12, 15, 36) = 180 units

⇒ Efficiency of B = 180 ÷ (15/2) = (180 × 2) ÷ 15 = 24

⇒ Efficiency of B + C = 180 ÷ (36/5) = (180 × 5) ÷ 36 = 25

⇒ Efficiency of C = (Efficiency of B + C) − (Efficiency of B)

⇒ Efficiency of C = 25 − 24 = 1

⇒ Time taken by C alone = Total Work ÷ Efficiency of C

⇒ Time taken by C alone = 180 ÷ 1 = 180 days

∴ The correct answer is 180 days.

Additional Information

LCM of Fractions

To find the LCM of fractions, calculate (LCM of Numerators) ÷ (HCF of Denominators).

Work and Wages

Wages are always distributed in the ratio of the efficiency of the workers or the work done by them.

Inverse Relation

Efficiency is inversely proportional to the time taken to complete a specific task. If Time ratio is x:y, Efficiency ratio is y:x.

Question 755

SBI Clerk 2025• Numerical Ability

Directions: Read the data carefully and answer the following questions.

The following table shows the number of candidates visiting three colleges (A, B, and C) as exam centers over three years (2020, 2021, and 2022):

College202020212022
A455260
B384755
C425058

The average number of candidates who visited College C over the three years is what percentage of the total number of candidates who visited all three colleges in 2022?

  1. AOption (a)

    28.90%

  2. BOption (b)

    32.50%

  3. COption (c)

    34.80%

  4. DOption (d)

    37.30%

  5. EOption (e)

    41.20%

View answer & explanation

Correct answer

Answer: (a)A.

28.90%

Why this answer is correct

College C total = 42 (2020) + 50 (2021) + 58 (2022) = 42 + 50 + 58 = 150

Average = 150 / 3 = 50

Total candidates in 2022 = College A (60) + College B (55) + College C (58) = 60 + 55 + 58 = 173

Percentage = 50 / 173 × 100 = 28.90%

Thus, the correct answer is 28.90%

Question 756

SBI Clerk 2025• Numerical Ability

Directions: Read the data carefully and answer the following questions.

The following table shows the number of candidates visiting three colleges (A, B, and C) as exam centers over three years (2020, 2021, and 2022):

College202020212022
A455260
B384755
C425058

What is the difference between the number of candidates who visited College C in 2021 and College B in 2020, and what is the ratio of this difference to the number of candidates who visited College A in 2021?

  1. AOption (a)

    7, 7 : 52

  2. BOption (b)

    8, 2 : 13

  3. COption (c)

    9, 9 : 52

  4. DOption (d)

    10, 5 : 26

  5. EOption (e)

    12, 3 : 13

View answer & explanation

Correct answer

Answer: (e)E.

12, 3 : 13

Why this answer is correct

College C in 2021 = 50

College B in 2020 = 38

Difference = 50 − 38 = 12

College A in 2021 = 52

Ratio = 12 / 52 or 12:52 = 3:13

Hence the correct answer is 12, 3:13

Question 757

SBI Clerk 2025• Numerical Ability

Directions: Read the data carefully and answer the following questions.

The following table shows the number of candidates visiting three colleges (A, B, and C) as exam centers over three years (2020, 2021, and 2022):

College202020212022
A455260
B384755
C425058

Which college had the highest total number of candidates visiting over the three years?

  1. AOption (a)

    College A

  2. BOption (b)

    College B

  3. COption (c)

    College C

  4. DOption (d)

    Both A and C

  5. EOption (e)

    Both B and C

View answer & explanation

Correct answer

Answer: (a)A.

College A

Why this answer is correct

College with the highest total number of candidates visiting over the three years:

College A: 

2020 = 45

2021 = 52

2022 = 60

Total = 45 + 52 + 60 = 157

College B:

2020 = 38

2021 = 47

2022 = 55

Total = 38 + 47 + 55 = 140

College C:

2020 = 42

2021 = 50

2022 = 58

Total = 42 + 50 + 58 = 150

College A (157 candidates) had the highest total number of candidates visiting over the three years.

Question 758

SBI Clerk 2025• Numerical Ability

Directions: Read the data carefully and answer the following questions.

The following table shows the number of candidates visiting three colleges (A, B, and C) as exam centers over three years (2020, 2021, and 2022):

College202020212022
A455260
B384755
C425058

The number of candidates who visited College B in 2020 is what percentage less than the number of candidates who visited College A in 2022?

  1. AOption (a)

    33.33%

  2. BOption (b)

    36.67%

  3. COption (c)

    40.00%

  4. DOption (d)

    43.33%

  5. EOption (e)

    46.67%

View answer & explanation

Correct answer

Answer: (b)B.

36.67%

Why this answer is correct

College B in 2020 = 38

College A in 2022 = 60

Difference = 60 − 38 = 22

Percentage less = 22 / 60 × 100 = 36.67%

Thus, the correct answer is 36.67%

Question 759

SBI Clerk 2025• Numerical Ability

Directions: Read the data carefully and answer the following questions.

The following table shows the number of candidates visiting three colleges (A, B, and C) as exam centers over three years (2020, 2021, and 2022):

College202020212022
A455260
B384755
C425058

What is the ratio of the total number of candidates who visited College A over the three years to the total number of candidates who visited College C over the three years?

  1. AOption (a)

    150:157

  2. BOption (b)

    157:150

  3. COption (c)

    14:15

  4. DOption (d)

    157:140

  5. EOption (e)

    15:14

View answer & explanation

Correct answer

Answer: (b)B.

157:150

Why this answer is correct

Total for College A = 45 + 52 + 60 = 157

Total for College C = 42 + 50 + 58 = 150

Ratio = 157:150

Thus, the correct answer is 157:150.

Question 760

SBI Clerk 2025• Numerical Ability

Find the wrong number in the following series:

2880, 480, 96, 24, 6, 4

  1. AOption (a)

    480

  2. BOption (b)

    96

  3. COption (c)

    24

  4. DOption (d)

    6

  5. EOption (e)

    4

View answer & explanation

Correct answer

Answer: (d)D.

6

Why this answer is correct

Solution:

Given Series: 2880, 480, 96, 24, 6, 2

Logic Used:

2880 ÷ 6 = 480 

480 ÷ 5 = 96 

96 ÷ 4 = 24 

24 ÷ 3 = 8  (given 6 instead of 8)

8 ÷ 2 = 4 

∴ The wrong number in the series is 6.

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