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Question 731

SBI Clerk 2025• Numerical Ability

A product costs 6000 Rs. It is sold at a 20% loss. From the selling price, a new product is bought and sold at a 40% profit. What is the overall profit (in Rs) on the whole transaction?

  1. AOption (a)

    120 Rs

  2. BOption (b)

    240 Rs

  3. COption (c)

    360 Rs

  4. DOption (d)

    480 Rs

  5. EOption (e)

    720 Rs

View answer & explanation

Correct answer

Answer: (e)E.

720 Rs

Why this answer is correct

Shortcut Trick

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

Here, a = −20% (loss) and b = +40% (profit).

Net profit% = −20 + 40 + (−20 × 40) ÷ 100 = 20 − 8 = 12%.

Overall profit = 12% of 6000 = 0.12 × 6000 = 720.

∴ The correct answer is 720 Rs.

Alternate Method

Given → Initial Cost Price (CP1) = 6000 Rs, Loss% = 20%, Profit% on second item = 40%. Formulas: SP = CP × (100 ± Gain/Loss)% ÷ 100 | Overall Profit = Final SP − Initial CP.

⇒ Selling Price of first product (SP1) = 6000 × (100 − 20) ÷ 100 = 6000 × 0.8 = 4800 Rs.

⇒ Cost Price of second product (CP2) = SP1 = 4800 Rs.

⇒ Selling Price of second product (SP2) = 4800 × (100 + 40) ÷ 100 = 4800 × 1.4 = 6720 Rs.

⇒ Overall Profit = Final SP − Initial CP = 6720 − 6000 = 720 Rs.

∴ The correct answer is 720 Rs.

Additional Information

Successive Percentage Change

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

Profit and Loss Basics

Profit occurs when SP > CP. Loss occurs when CP > SP. Both are always calculated on the CP unless stated otherwise.

Question 732

SBI Clerk 2025• Numerical Ability

A invests ₹2400 for 12 months. After 8 months, B joins with an investment of ₹x. After one year, the profit of B is 3/11 of the total profit. Find the value of x.

  1. AOption (a)

    ₹1800

  2. BOption (b)

    ₹2700

  3. COption (c)

    ₹2200

  4. DOption (d)

    ₹2400

  5. EOption (e)

    ₹1900

View answer & explanation

Correct answer

Answer: (b)B.

₹2700

Why this answer is correct

Shortcut Trick

Ratio of Profit of B to Total = 3 : 11, so ratio of Profit A : B = (11 − 3) : 3 = 8 : 3.

Ratio of Investments × Time = Profit Ratio.

(2400 × 12) ÷ (x × 4) = 8 ÷ 3.

(600 × 12) ÷ x = 8 ÷ 3 ⇒ 7200 ÷ x = 8 ÷ 3.

x = (7200 × 3) ÷ 8 = 900 × 3 = 2700.

∴ The correct answer is ₹2700.

Alternate Method

Given → Investment of A = ₹2400, Time of A = 12 months, Time of B = 12 − 8 = 4 months. Profit of B = 3/11 of Total. Formulas: Profit Ratio = (InvestmentA × TimeA) : (InvestmentB × TimeB).

⇒ Total Profit = 11 units, B Profit = 3 units, A Profit = 11 − 3 = 8 units. ⇒ (2400 × 12) ÷ (x × 4) = 8 ÷ 3 ⇒ 28800 ÷ 4x = 8 ÷ 3 ⇒ 7200 ÷ x = 8 ÷ 3 ⇒ 8x = 21600 ⇒ x = 2700.

∴ The correct answer is ₹2700.

Additional Information

Partnership Concept

When multiple persons invest capital for different time periods, the profit is distributed in the ratio of the product of their capital and time.

Investment Formula

Investment = Profit ÷ Time. If the profit ratio and time ratio are known, the investment ratio can be calculated directly.

Question 733

SBI Clerk 2025• Numerical Ability

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

The line graph represents the sum of Fine Art and Visual Art and only Visual Art across 5 exhibitions.

Total Arts = Fine Arts + Visual Arts

The number of fine arts in T is what percent of the total number of arts in same exhibition?

  1. AOption (a)

    45%

  2. BOption (b)

    40%

  3. COption (c)

    60%

  4. DOption (d)

    55%

  5. EOption (e)

    30%

View answer & explanation

Correct answer

Answer: (a)A.

45%

Why this answer is correct

General Solution:

The given data represents the Total Arts and Visual Arts across 5 exhibitions (P, Q, R, S, T). From this, we can derive the Fine Arts for each exhibition using the formula:

Fine Arts = Total Arts − Visual Arts

Using the formula above, we calculate the Fine Arts for each exhibition:

Exhibition P:

Fine Arts = 114 − 45 = 69

Exhibition Q:

Fine Arts = 108 − 54 = 54

Exhibition R:

Fine Arts = 125 − 65 = 60

Exhibition S:

Fine Arts = 96 − 60 = 36

Exhibition T:

Fine Arts = 120 − 66 = 54

Thus,

ExhibitionTotal ArtsVisual ArtsFine Arts
P1144569
Q1085454
R1256560
S966036
T1206654

 

Calculations:

The formula to calculate the percentage is:

Percentage = (Part / Whole) × 100

Here:

Part = Fine Arts in T = 54

Whole = Total Arts in T = 120

Substitute the values into the formula:

Percentage = (54 / 120) × 100 = 45%.

Thus, the correct answer is 45%

Question 734

SBI Clerk 2025• Numerical Ability

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

The line graph represents the sum of Fine Art and Visual Art and only Visual Art across 5 exhibitions.

Total Arts = Fine Arts + Visual Arts

The total number of arts in T is equal to the sum of the visual arts in which one of the following pairs?

  1. AOption (a)

    S and T

  2. BOption (b)

    P and R

  3. COption (c)

    Q and T

  4. DOption (d)

    Q and R

  5. EOption (e)

    P and S

View answer & explanation

Correct answer

Answer: (c)C.

Q and T

Why this answer is correct

General Solution:

The given data represents the Total Arts and Visual Arts across 5 exhibitions (P, Q, R, S, T). From this, we can derive the Fine Arts for each exhibition using the formula:

Fine Arts = Total Arts − Visual Arts

Using the formula above, we calculate the Fine Arts for each exhibition:

Exhibition P:

Fine Arts = 114 − 45 = 69

Exhibition Q:

Fine Arts = 108 − 54 = 54

Exhibition R:

Fine Arts = 125 − 65 = 60

Exhibition S:

Fine Arts = 96 − 60 = 36

Exhibition T:

Fine Arts = 120 − 66 = 54

Thus,

ExhibitionTotal ArtsVisual ArtsFine Arts
P1144569
Q1085454
R1256560
S966036
T1206654

 

Calculations:

From the table:

Total Arts in T = 120

We need to check the sum of Visual Arts for each pair of exhibitions and see which one equals 120.

Pair 1: S and T

Visual Arts in S = 60

Visual Arts in T = 66

Total = 60 + 66 = 126

126 ≠ 120 → Not a match.

Pair 2: P and R

Visual Arts in P = 45

Visual Arts in R = 65

Total = 45 + 65 = 110

110 ≠ 120 → Not a match.

Pair 3: Q and T

Visual Arts in Q = 54

Visual Arts in T = 66

Total = 54 + 66 = 120

120 = 120 → Match!

Pair 4: Q and R

Visual Arts in Q = 54

Visual Arts in R = 65

Total = 54 + 65 = 119

119 ≠ 120 → Not a match.

Pair 5: P and S

Visual Arts in P = 45

Visual Arts in S = 60

Total = 45 + 60 = 105

105 ≠ 120 → Not a match.

The pair Q and T has a sum of Visual Arts equal to the Total Arts in Exhibition T.

Question 735

SBI Clerk 2025• Numerical Ability

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

The line graph represents the sum of Fine Art and Visual Art and only Visual Art across 5 exhibitions.

Total Arts = Fine Arts + Visual Arts

Find the ratio of the number of fine arts in R and T together to the number of total arts in P.

  1. AOption (a)

    5:6

  2. BOption (b)

    2:3

  3. COption (c)

    1:1

  4. DOption (d)

    6:5

  5. EOption (e)

    3:2

View answer & explanation

Correct answer

Answer: (c)C.

1:1

Why this answer is correct

General Solution:

The given data represents the Total Arts and Visual Arts across 5 exhibitions (P, Q, R, S, T). From this, we can derive the Fine Arts for each exhibition using the formula:

Fine Arts = Total Arts − Visual Arts

Using the formula above, we calculate the Fine Arts for each exhibition:

Exhibition P:

Fine Arts = 114 − 45 = 69

Exhibition Q:

Fine Arts = 108 − 54 = 54

Exhibition R:

Fine Arts = 125 − 65 = 60

Exhibition S:

Fine Arts = 96 − 60 = 36

Exhibition T:

Fine Arts = 120 − 66 = 54

Thus,

ExhibitionTotal ArtsVisual ArtsFine Arts
P1144569
Q1085454
R1256560
S966036
T1206654

 

Calculations:

From the table:

Fine Arts in R and T together:

Fine Arts in R = 60

Fine Arts in T = 54

Total Fine Arts in R and T = 60 + 54 = 114

Total Arts in P = 114

The ratio of the number of Fine Arts in R and T together to the number of Total Arts in P is:

Ratio = Fine Arts in R and T / Total Arts in P = 114 / 1 = 1:1

Thus, the correct answer is 1:1.

Question 736

SBI Clerk 2025• Numerical Ability

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

The line graph represents the sum of Fine Art and Visual Art and only Visual Art across 5 exhibitions.

Total Arts = Fine Arts + Visual Arts

Find the total number of fine arts in P and R together.

  1. AOption (a)

    115

  2. BOption (b)

    129

  3. COption (c)

    108

  4. DOption (d)

    123

  5. EOption (e)

    None of these

View answer & explanation

Correct answer

Answer: (b)B.

129

Why this answer is correct

General Solution:

The given data represents the Total Arts and Visual Arts across 5 exhibitions (P, Q, R, S, T). From this, we can derive the Fine Arts for each exhibition using the formula:

Fine Arts = Total Arts − Visual Arts

Using the formula above, we calculate the Fine Arts for each exhibition:

Exhibition P:

Fine Arts = 114 − 45 = 69

Exhibition Q:

Fine Arts = 108 − 54 = 54

Exhibition R:

Fine Arts = 125 − 65 = 60

Exhibition S:

Fine Arts = 96 − 60 = 36

Exhibition T:

Fine Arts = 120 − 66 = 54

Thus,

ExhibitionTotal ArtsVisual ArtsFine Arts
P1144569
Q1085454
R1256560
S966036
T1206654

 

Calculations:

From the table, we know the Fine Arts for each exhibition:

Exhibition P: Fine Arts = 69

Exhibition R: Fine Arts = 60

To find the total number of Fine Arts in P and R together, we add the Fine Arts of P and R:

Total Fine Arts (P + R) = 69 + 60 = 129

Thus, the total number of Fine Arts in P and R together is 129.

Question 737

SBI Clerk 2025• Numerical Ability

In a factory 50% of the workers are above 45 years and of these 60 % are female and the rest are male. If there are 1200 female workers above 45 years then find the total number of workers in the factory?

  1. AOption (a)

    4500

  2. BOption (b)

    4600

  3. COption (c)

    4000

  4. DOption (d)

    4100

  5. EOption (e)

    4200

View answer & explanation

Correct answer

Answer: (c)C.

4000

Why this answer is correct

Shortcut Trick

Let total workers be 100%.

Workers above 45 years = 50%.

Female workers above 45 = 60% of 50% = 30%.

Given, 30% = 1200 ⇒ 1% = 40.

Total workers = 100% = 100 × 40 = 4000.

∴ The correct answer is 4000 workers.

Alternate Method

Given: Female workers above 45 = 1200; % Above 45 = 50%; % Female in that group = 60%.

Formula: Total Workers × % Above 45 × % Female = 1200

⇒ Let Total workers be x.

⇒ x × (50/100) × (60/100) = 1200

⇒ x × (1/2) × (3/5) = 1200

⇒ x × (3/10) = 1200

⇒ x = (1200 × 10) ÷ 3

⇒ x = 400 × 10 = 4000

∴ The correct answer is 4000 workers.

Additional Information

Successive Percentage Change

When percentages are applied sequentially on a base value, the effective percentage is P1 × P2 / 100.

Base Value Concept

Always identify the base (100%) correctly; in this case, females are 60% of the 50% subset, not the whole population.

Question 738

SBI Clerk 2025• Numerical Ability

Rakesh invested Rs. 12000 in two different schemes. First at 10% per annum, rest at 20% per annum and thus in 4 years the total interest from both the amounts collected was Rs. 6720. What was the amount lent out @ 20% per annum?

  1. AOption (a)

    Rs. 4600

  2. BOption (b)

    Rs. 4400

  3. COption (c)

    Rs. 4800

  4. DOption (d)

    Rs. 5000

  5. EOption (e)

    None of these

View answer & explanation

Correct answer

Answer: (c)C.

Rs. 4800

Why this answer is correct

Shortcut Trick

Overall interest rate per annum = (6720 ÷ 4) × 100 ÷ 12000 = 14%.

Using Alligation: (Scheme 1: 10%) vs (Scheme 2: 20%) with Mean (14%).

Ratio of investments = (20 − 14) : (14 − 10) = 6 : 4 = 3 : 2.

Amount @ 20% = (2 ÷ 5) × 12000 = 4800.

∴ The correct answer is Rs. 4800.

Alternate Method

Given: Total Principal (P) = Rs. 12000, Total SI = Rs. 6720, Time (T) = 4 years, R1 = 10%, R2 = 20%.

Formula: SI = (P × R × T) ÷ 100

⇒ Let the amount lent at 20% be Rs. x.

⇒ Amount lent at 10% = (12000 − x).

⇒ [(12000 − x) × 10 × 4] ÷ 100 + [x × 20 × 4] ÷ 100 = 6720

⇒ (12000 − x) × 40 + 80x = 672000

⇒ 480000 − 40x + 80x = 672000

⇒ 40x = 672000 − 480000

⇒ 40x = 192000

⇒ x = 192000 ÷ 40 = 4800

∴ The correct answer is Rs. 4800.

Additional Information

Simple Interest (SI)

The interest remains constant every year on the original principal. SI = (P × R × T) ÷ 100.

Alligation in Interest

When a sum is divided into two parts with different rates, the ratio of parts = (Rate2 − Avg Rate) : (Avg Rate − Rate1).

Effective Annual Rate

If interest is calculated for multiple years, the total percentage interest is R × T%.

Question 739

SBI Clerk 2025• Numerical Ability

Mohan is 12 years younger than Krishna. Mohan's age is 40% of the sum of his and Krishna's age.  what will be Mohan's age after 8 years? 

  1. AOption (a)

    24 years

  2. BOption (b)

    36 years

  3. COption (c)

    32 years

  4. DOption (d)

    30 years

  5. EOption (e)

    31 years

View answer & explanation

Correct answer

Answer: (c)C.

32 years

Why this answer is correct

Shortcut Trick

Ratio of Mohan's age to (Mohan + Krishna) = 40% = 2 : 5.

If Mohan = 2 units and Sum = 5 units, then Krishna = 5 − 2 = 3 units.

Difference = 3 − 2 = 1 unit → 12 years.

Mohan's current age = 2 × 12 = 24 years.

Mohan's age after 8 years = 24 + 8 = 32 years.

∴ The correct answer is 32 years.

Alternate Method

Given: Krishna = Mohan + 12

Formula: Mohan = 0.40 × (Mohan + Krishna)

⇒ M = 0.4(M + M + 12)

⇒ M = 0.4(2M + 12)

⇒ M = 0.8M + 4.8

⇒ 0.2M = 4.8

⇒ M = 4.8 ÷ 0.2 = 24 years

⇒ Age after 8 years = 24 + 8 = 32 years

∴ The correct answer is 32 years.

Additional Information

Age Difference Property

The difference between the ages of two persons remains constant throughout their lives, regardless of the number of years passed.

Percentage to Ratio Conversion

Always convert percentages to simple fractions (e.g., 40% = 2/5) to solve ratio-based age problems faster without using variables.

Question 740

SBI Clerk 2025• Numerical Ability

The length of a rectangle is four times its breadth. If its length is increased by 20 cm. and breadth is increased by 30 cm, the area of the rectangle is increased by 880 cm2. Find the length of the rectangle.

  1. AOption (a)

    12 cm

  2. BOption (b)

    10 cm

  3. COption (c)

    15 cm

  4. DOption (d)

    8 cm

  5. EOption (e)

    6 cm

View answer & explanation

Correct answer

Answer: (d)D.

8 cm

Why this answer is correct

Shortcut Trick

Let breadth = x and length = 4x.

New Area − Old Area = 880

(4x + 20)(x + 30) − 4x2 = 880

120x + 20x + 600 = 880 ⇒ 140x = 280 ⇒ x = 2 cm.

Length = 4 × 2 = 8 cm.

∴ The correct answer is 8 cm.

Alternate Method

Given: Length (L) = 4 × Breadth (B); Lnew = L + 20; Bnew = B + 30; Area Increase = 880 cm2.

Formula: Area of Rectangle = Length × Breadth

⇒ Original Area = 4x × x = 4x2

⇒ New Area = (4x + 20)(x + 30) = 4x2 + 120x + 20x + 600

⇒ (4x2 + 140x + 600) − 4x2 = 880

⇒ 140x + 600 = 880

⇒ 140x = 280

⇒ x = 2 cm

⇒ Length = 4x = 4 × 2 = 8 cm

∴ The correct answer is 8 cm.

Additional Information

Perimeter of Rectangle

The total boundary length of a rectangle is given by 2 × (Length + Breadth).

Diagonal of Rectangle

The distance between opposite corners is calculated using Pythagoras theorem: d = √(L2 + B2).

Area Change Percentage

If length increases by a% and breadth by b%, net area change % = a + b + (a × b)/100.

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