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Question 451

SBI Clerk 2025• Numerical Ability

A car travels at a speed of 24 km/hr and covers a distance of 84 km. After that, the car increases its speed by 25% and covers the next 150 km. What is the total time taken for the entire journey?

  1. AOption (a)

    8.5 hours

  2. BOption (b)

    9.25 hours

  3. COption (c)

    10.75 hours

  4. DOption (d)

    11.5 hours

  5. EOption (e)

    None of these

View answer & explanation

Correct answer

Answer: (a)A.

8.5 hours

Why this answer is correct

Shortcut Trick

First part time = 84 ÷ 24 = 3.5 hr

New speed = 24 × 1.25 = 30 km/hr

Second part time = 150 ÷ 30 = 5 hr

Total time = 3.5 + 5 = 8.5 hr

∴ The correct answer is 8.5 hr.

Alternate Method

Given: First distance (D1) = 84 km, First speed (S1) = 24 km/hr, Second distance (D2) = 150 km.

Formula Used: Time = Distance ÷ Speed

⇒ Time for first part (T1) = D1 ÷ S1

⇒ T1 = 84 ÷ 24 = 3.5 hr

⇒ Increased speed (S2) = S1 + (25% of S1)

⇒ S2 = 24 + (25/100 × 24) = 24 + 6 = 30 km/hr

⇒ Time for second part (T2) = D2 ÷ S2

⇒ T2 = 150 ÷ 30 = 5 hr

⇒ Total Time = T1 + T2 = 3.5 + 5 = 8.5 hr

∴ The correct answer is 8.5 hr.

Additional Information

Average Speed Formula

Average Speed = Total Distance ÷ Total Time. For this journey, Average Speed = (84 + 150) ÷ 8.5 ≈ 27.53 km/hr.

Percentage Increase in Speed

When speed increases by x%, the new speed is S × (1 + x/100). Here, 24 × (1 + 0.25) = 24 × 1.25 = 30 km/hr.

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 452

SBI Clerk 2025• Numerical Ability

A person spends 20% of their salary on rent. Out of the remaining salary, 30% is spent on Food, 25% is spent on Transport, and the rest is spent on Entertainment. If the amount spent on Entertainment is ₹16,560, what is the total salary of the person?

  1. AOption (a)

    ₹69,000

  2. BOption (b)

    ₹56,000

  3. COption (c)

    ₹35,000

  4. DOption (d)

    ₹46,000

  5. EOption (e)

    ₹72,000

View answer & explanation

Correct answer

Answer: (d)D.

₹46,000

Why this answer is correct

Let the total salary be S.

Amount spent on rent =20% of S.

Remaining salary after rent = 80% of S.

Amount spent on Food = 30% of the remaining salary.

Amount spent on Transport = 25% of the remaining salary.

Amount spent on Entertainment = Remaining percentage of the remaining salary.

Total percentage spent on Food and Transport = 30% + 25% = 55% 

Percentage spent on Entertainment = 100% - 55% = 45%.

Entertainment = 45%of the remaining salary.

Given that Entertainment = ₹16,560:

45% of 80% of S = 16,560

0.45 × 0.8 × S = 16,560

0.36 × S = 16,560

S = 16,560 / 0.36

S = 46,000

Thus, the total salary of the person is ₹46,000.

Question 453

SBI Clerk 2025• Numerical Ability

The ratio of the diameter of a circle to the breadth of a rectangle is 7:4. The area of the circle is 616 cm². If the length of the rectangle is 6 cm more than its breadth, what is the area of the rectangle?

  1. AOption (a)

    268 cm2

  2. BOption (b)

    286 cm2

  3. COption (c)

    305 cm2

  4. DOption (d)

    352 cm2

  5. EOption (e)

    346 cm2

View answer & explanation

Correct answer

Answer: (d)D.

352 cm2

Why this answer is correct

Shortcut Trick

Area of circle 616 cm2 → Radius (r) = 14 cm, Diameter (d) = 28 cm.

Ratio Diameter : Breadth = 7 : 4 ⇒ 7 units = 28 cm ⇒ 1 unit = 4 cm.

Breadth (b) = 4 × 4 = 16 cm; Length (l) = 16 + 6 = 22 cm.

Area of rectangle = 22 × 16 = 352 cm2.

∴ The correct answer is 352 cm2.

Alternate Method

Given: Area of circle = 616 cm2, Ratio d : b = 7 : 4, l = b + 6.

Formula Used: Area of Circle = πr2; Area of Rectangle = l × b.

⇒ πr2 = 616

⇒ (22/7) × r2 = 616

⇒ r2 = (616 × 7) ÷ 22 = 28 × 7 = 196

⇒ Radius (r) = 14 cm ∴ Diameter (d) = 28 cm

⇒ Diameter : Breadth = 7 : 4 ⇒ 28 : b = 7 : 4

⇒ Breadth (b) = (28 × 4) ÷ 7 = 16 cm

⇒ Length (l) = 16 + 6 = 22 cm

⇒ Area of rectangle = 22 × 16 = 352 cm2

∴ The correct answer is 352 cm2.

Additional Information

Circle Properties

Circumference = 2πr and Diameter = 2r. For r = 7, Area = 154; for r = 14, Area = 616.

Rectangle Perimeter

Perimeter of a rectangle is given by 2(l + b), where l is length and b is breadth.

Ratio Applications

If a : b = x : y, then a = kx and b = ky where k is a constant proportionality factor.

Question 454

SBI Clerk 2025• Numerical Ability

The table shows the number movie shows in three months [January, February and March] in three different multiplexes [A, B, and C].

MonthsABC
January180270140
February160210200
March150220240

Find the difference between total number of movies shows in February and March in all multiplex together?

  1. AOption (a)

    45

  2. BOption (b)

    56

  3. COption (c)

    40

  4. DOption (d)

    85

  5. EOption (e)

    70

View answer & explanation

Correct answer

Answer: (c)C.

40

Why this answer is correct

Calculation:

Total shows in February = 160 + 210 + 200 = 570

Total shows in March = 150 + 220 + 240 = 610

Difference = Total shows in March - Total shows in February

⇒ 610 - 570 = 40

∴ The difference between the total number of movie shows in February and March across all multiplexes is 40.

Question 455

SBI Clerk 2025• Numerical Ability

The table shows the number movie shows in three months [January, February and March] in three different multiplexes [A, B, and C].

MonthsABC
January180270140
February160210200
March150220240

Number movie shows in January at D is 5/7th of the number of movies shows in January at C. Find number the number of movies shows at D in January?

  1. AOption (a)

    120

  2. BOption (b)

    140

  3. COption (c)

    150

  4. DOption (d)

    100

  5. EOption (e)

    160

View answer & explanation

Correct answer

Answer: (d)D.

100

Why this answer is correct

Calculation:

Number of movie shows in January at multiplex C = 140

Number of movie shows in January at D is 5/7th of that at C.

We need to find the number of movie shows at D in January.

Shows at D = (5/7) × Shows at C

⇒ (5/7) × 140

⇒ 700 / 7

⇒ 100

∴ The number of movie shows in January at D is 100.

Question 456

SBI Clerk 2025• Numerical Ability

The table shows the number movie shows in three months [January, February and March] in three different multiplexes [A, B, and C].

MonthsABC
January180270140
February160210200
March150220240

Find the ratio of total number of shows in January and February together in B and in February and March together in C?

  1. AOption (a)

    12 : 11

  2. BOption (b)

    11 : 12

  3. COption (c)

    12 : 13

  4. DOption (d)

    13 : 12

  5. EOption (e)

    5 : 6

View answer & explanation

Correct answer

Answer: (a)A.

12 : 11

Why this answer is correct

Calculation:

Total shows in January and February at B = 270 + 210 = 480

Total shows in February and March at C = 200 + 240 = 440

Required Ratio = (Total shows in B for January & February) : (Total shows in C for February & March)

⇒ 480 : 440

⇒ 12 : 11

∴ The required ratio is 12 : 11.

Question 457

SBI Clerk 2025• Numerical Ability

The table shows the number movie shows in three months [January, February and March] in three different multiplexes [A, B, and C].

MonthsABC
January180270140
February160210200
March150220240

Number of movies shows in April at C is 25% more than the number of movies shows in March at same multiplex, Find the number of movies shows in April at C?

  1. AOption (a)

    250

  2. BOption (b)

    300

  3. COption (c)

    320

  4. DOption (d)

    280

  5. EOption (e)

    340

View answer & explanation

Correct answer

Answer: (b)B.

300

Why this answer is correct

Calculation:

Number of movie shows in March at multiplex C = 240

Number of movie shows in April at C is 25% more than in March.

Number of shows in April at C:

⇒ 240 × (1 + 25/100)

⇒ 240 × (1 + 0.25)

⇒ 240 × 1.25

⇒ 300

∴ The number of movie shows in April at C is 300.

Question 458

SBI Clerk 2025• Numerical Ability

The table shows the number movie shows in three months [January, February and March] in three different multiplexes [A, B, and C].

MonthsABC
January180270140
February160210200
March150220240

Total number of movies shows in January and February at A is how much less than the number of movies in same months at B?

  1. AOption (a)

    120

  2. BOption (b)

    165

  3. COption (c)

    160

  4. DOption (d)

    170

  5. EOption (e)

    140

View answer & explanation

Correct answer

Answer: (e)E.

140

Why this answer is correct

Calculation:

Total shows at A:

⇒ 180 + 160 = 340

Total shows at B:

⇒ 270 + 210 = 480

Difference = Total shows at B - Total shows at A

⇒ 480 - 340 = 140

∴ The number of movie shows in January and February at A is 140 less than at B.

Question 459

SBI Clerk 2025• Numerical Ability

30% of a principal is invested at 12% per annum, and 70% of the principal is invested at 8% per annum. The sum of the interests earned from both investments is 2438. What is the principal?

  1. AOption (a)

    30,000

  2. BOption (b)

    22,750

  3. COption (c)

    26,500

  4. DOption (d)

    28,000

  5. EOption (e)

    None of these

View answer & explanation

Correct answer

Answer: (c)C.

26,500

Why this answer is correct

Shortcut Trick

Let the total principal be 100 units.

Weighted Interest Rate = (30% × 12%) + (70% × 8%) = 3.6% + 5.6% = 9.2%.

9.2% of Principal = 2438

Principal = 2438 ÷ 0.092 = 26500.

∴ The correct answer is 26,500.

Alternate Method

Given: Interest 1 (at 12%) + Interest 2 (at 8%) = 2438.

Formula Used: Simple Interest (SI) = (P × R × T) ÷ 100

⇒ Let Principal be P.

⇒ SI1 = (0.30P × 12 × 1) ÷ 100 = 0.036P

⇒ SI2 = (0.70P × 8 × 1) ÷ 100 = 0.056P

⇒ Total Interest = 0.036P + 0.056P = 0.092P

⇒ 0.092P = 2438

⇒ P = 2438 ÷ 0.092 = 26500

∴ The correct answer is 26,500.

Additional Information

Weighted Average Rate of Interest

When a principal is divided, the effective rate Reff = (w1r1 + w2r2 + ...), where w is the weightage of each part.

Simple Interest Properties

Simple interest is calculated only on the original principal. Interest remains constant every year if the rate and principal are unchanged.

Question 460

SBI Clerk 2025• Numerical Ability

A, B, and C can complete a work individually in 48 days, 72 days, and 54 days, respectively. A and B work together for 16 days, and the remaining work is completed by C alone. How many days will C take to complete the work?

  1. AOption (a)

    22 days

  2. BOption (b)

    24 days

  3. COption (c)

    26 days

  4. DOption (d)

    28 days

  5. EOption (e)

    18 days

View answer & explanation

Correct answer

Answer: (b)B.

24 days

Why this answer is correct

Shortcut Trick

Total Work (LCM of 48, 72, 54) = 432 units.

Efficiencies: A = 9, B = 6, C = 8.

Work done by (A + B) in 16 days = (9 + 6) × 16 = 15 × 16 = 240 units.

Remaining Work = 432 − 240 = 192 units.

Time taken by C = 192 ÷ 8 = 24 days.

∴ The correct answer is 24 days.

Alternate Method

Given: Individual time of A = 48 days, B = 72 days, C = 54 days.

Formula Used: Efficiency = Total Work ÷ Time; Work Done = Efficiency × Time.

PersonDaysTotal WorkEfficiency
A484329
B726
C548

⇒ Total work = LCM(48, 72, 54) = 432 units.

⇒ Combined Efficiency of A and B = 9 + 6 = 15 units/day.

⇒ Work completed by A and B in 16 days = 15 × 16 = 240 units.

⇒ Remaining Work = 432 − 240 = 192 units.

⇒ Days taken by C to finish remaining work = 192 ÷ 8 = 24 days.

∴ The correct answer is 24 days.

Additional Information

Pipes & Cisterns

Conceptually identical to Time & Work, where inlet pipes have positive efficiency and outlet pipes have negative efficiency.

Work and Wages

Wages are distributed in the ratio of the actual work done by each person, or in the ratio of their efficiencies if they work for the same duration.

Alternate Day Work

Calculate the work done in one cycle (sum of efficiencies over the cycle period) and then divide the total work by the cycle total.

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