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Given:

Cost price of article = a + 1000

Profit = Rs. 1000

Discount = 12.5%

Solution:

Marked price = 160%  of (a + 1000) = 8/5(a + 1000)

Selling price = 7/8 of (8/5(a + 1000) = 7/5 of (a + 1000)   (12.5% = 1/8)

Now,

Profit = SP - CP

1000 = 7/5of (a + 1000) - (a +1000)

1000 = (2a + 2000)/5

2a + 2000 = 5000

2a = 3000

a = 1500

Selling price of X = 7/5(a + 1000) = 3500

Now,

Cost price = a + 500 = 2000

Selling price of B is 14.28% less than selling price of article X

Selling price = 6/7 x 3500  (14.28% = 1/7)

= 3000

Profit% = (SP - CP)/CP x100 = (3000 - 2000)/2000 x 100 = 50%

Hence option (3) is correct.

Given:

The expression $\frac{1}{7} \times \frac{1}{8} \div \frac{72}{51}$ of $\left(\frac{1}{9}+\frac{1}{8}\right)+\left(\frac{63}{56} \times \frac{48}{72}\right)$

Concept used:

⇒ BODMAS rule

Calculation:

⇒ $\frac{1}{7} \times \frac{1}{8} \div \frac{72}{51}$ of $(\frac{8 + 9 }{72}) + (\frac{9}{8} \times \frac{2}{3})$

⇒ $\frac{1}{7} \times \frac{1}{8} \div \frac{72}{51}$ of $\frac{17 }{72} + \frac{3}{4}$

⇒ $\frac{1}{7} \times \frac{1}{8} \div( \frac{72}{51} \times \frac{17}{72})$ $+ \ \frac{3}{4}$

⇒ $\frac{1}{7} \times( \frac{1}{8} \div \frac{1}{3}) + \frac{3}{4}$

⇒ $\frac{1}{7} \times \frac{3}{8} + \frac{3}{4}$

⇒ $\frac{3}{56} + \frac{3}{4}$

⇒ $\frac{45}{56}$

Hence, the value of expression is 45/56.

Given:

Discount = 10%, 15% and 10%

SP = 2754

Formula used:

Profit = SP – CP

Discount% = Discount/MP × 100

Calculation:

Let the marked price be MP 

⇒ MP × (9/10)(17/20)(9/10) = 2754

⇒ MP × 1377/2000 = 2754

MP = 4000

The answer is 4000.

Given:

X can do a work = 270 days

Concept used:

Total Work = Efficiency × Time

Calculation:

According to the question,

⇒ X × 270 = X × 55 + Y × 215

⇒ X × (270 - 55) = Y × 215

⇒ X × 215 = Y × 215

⇒ $\dfrac{\text{X}}{\text{Y}}$ =$\dfrac{215 }{215}$= $\dfrac{1 }{1}$

∴ Efficiency of X: Efficiency of Y = 1: 1

Now, Total work = X × 270 = 1 × 270 = 270 unit

Time is taken by X and Y together = $\dfrac{270 }{1+1}$ = $\dfrac{270 }{2}$ = 135 days

∴ The time is taken by X and Y together is 135 days.

Given:

Height = 5 m

Cost of whitewashing 4 walls at Rs. 2.50 per sq m = Rs. 200

Cost of carpeting the floor = Rs. 5/m²

Calculation:

Let breadth be x meter

⇒ Length = 3x meter

Area of 2 walls along length side = 2 × height × length = 2 × 5 × 3x = 30x

Area of 2 walls along breadth side = 2 × height × breadth = 2 × 5 × x = 10x

Total area of 4 walls = 30x + 10x = 40x

Now, 40x × Rs. 2.5 = Rs. 200

⇒ 40x = 80

⇒ x = 2

Breadth = 2 meter

Length = 2 × 3 = 6 meter

Now, area of floor = length × breadth = (6 × 2) m² = 12 m²

Cost of carpeting the floor at Rs. 5/m² = 12 × 5 = Rs. 60

∴ Cost of carpeting the floor is Rs. 60

Given:

Hours worked per day in first week = 4

Hours worked per day in second week = 5

Hours worked per day in third and fourth week = 6

Rate = Rs. 100 for every 30 minutes 

Concept:

In these type of questions we calculate total hours worked and multiply them by the rate.

Formula:

Amount = Total hours × Price per hour

Calculations:

Hours worked in first week = 4 × 7

⇒ 28 hours 

Hours worked in second week = 5 × 7

⇒ 35 hours

Hours worked in third week = 6 × 7

⇒ 42 hours 

Hours worked in fourth week = 6 × 7

⇒ 42 hours 

∴ Total hours worked = 28 + 35 + 42 + 42

⇒ 147 hours

Rate = Rs. 100 for every 30 minutes

⇒ Rs. 100 × 2 for every hour

⇒ Rs. 200 per hour

∴ Amount that the worker will receive = 147 × 200

⇒ Rs. 29400

DIRECTIONS: What approximate value will come in place of the question mark (?) in the following question?

√5456 × √2120 ÷ √460 = ?

Calculation:

First, approximate the square roots of the given numbers:

√5456 ≈ 74 (since 74 × 74 = 5476, which is close to 5456)

√2120 ≈ 46 (since 46 × 46 = 2116, which is close to 2120)

√460 ≈ 21.5 (since 21.5 × 21.5 = 462.25, which is close to 460)

Now, substitute these approximations into the equation:

√5456 × √2120 ÷ √460 ≈ 74 × 46 ÷ 21.5

Calculate the numerator:

74 × 46 = 3404

Now, divide by the denominator:

3404 ÷ 21.5 ≈ 158.32 ≈ 159

Therefore, the approximate value that will come in place of the question mark is 159.

Calculation

⇒ 1100% of 44 + 115% of 240 = ? - 24

⇒ 484 + 23 × 12 = ? - 24

⇒ 484 + 276 + 24 = ?

⇒ 784 = ?

The answer is 784.

Given:

Total number of 'Vadas' was 12.

Calculation:

Let's assume that the consecutive 3-even numbers be 2x, (2x + 2), (2x + 4)

Now, according to the question

⇒ 2x +  (2x + 2) + (2x + 4) = 12

⇒ 6x + 6 = 12

⇒ x = 1

So, the numbers are 2, 4, 6

∴ The maximum number of Vadas kept in a plate is 6

Shortcut Trick

Profit share is directly proportional to Capital × Time.

Aman's 1 profit ratio part = 4000 × 12 = 48000.

Bunty's profit (3 parts) = 3 × 48000 = 144000 ⇒ Bunty's Capital = 144000 ÷ 5 = Rs. 28800.

Chaman's profit (7 parts) = 7 × 48000 = 336000 ⇒ Chaman's Capital = 336000 ÷ 8 = Rs. 42000.

Difference in their capitals = 42000 − 28800 = 13200.

∴ The correct answer is Rs. 13200.

Alternate Method

Given:

Aman's Capital (C_A) = Rs. 4000

Time of investment for Aman (T_A) = 12 months

Bunty joined after 7 months, so Time (T_B) = 12 − 7 = 5 months

Chaman joined after 4 months, so Time (T_C) = 12 − 4 = 8 months

Profit Ratio = 1 : 3 : 7

Formula Used:

Profit Ratio = (C_A × T_A) : (C_B × T_B) : (C_C × T_C)

Aman Cap: ₹4000 Time: 12 mo

Ratio: 1 = 48000 units

Bunty Cap: ? Time: 5 mo

Ratio: 3 = 144000 units

Chaman Cap: ? Time: 8 mo

Ratio: 7 = 336000 units

Calculations:

⇒ Aman's profit equivalent = 4000 × 12 = 48000

⇒ As per the ratio, 1 unit of profit is represented by 48000.

⇒ Bunty's profit equivalent = 3 units = 3 × 48000 = 144000

⇒ Bunty's Capital × 5 = 144000

⇒ Bunty's Capital = 144000 ÷ 5 = 28800

⇒ Chaman's profit equivalent = 7 units = 7 × 48000 = 336000

⇒ Chaman's Capital × 8 = 336000

⇒ Chaman's Capital = 336000 ÷ 8 = 42000

⇒ Difference = 42000 − 28800 = 13200

∴ The correct answer is Rs. 13200.

Additional Information

Basic Profit Division Rule

If partners invest different amounts for varying time periods, the total profit is distributed in the ratio of the product of their invested capital and the duration of investment: (C₁ × T₁ : C₂ × T₂ : C₃ × T₃).

Equivalent Capital

Equivalent capital represents the total amount that would need to be invested for a standard unit of time (like 1 month) to yield the exact same final profit share.

Working vs Sleeping Partners

A working partner actively manages the business and usually takes a fixed percentage of the profit or a fixed salary before the rest of the profit is divided among all partners based on their investments. A sleeping partner merely invests capital.