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Shortcut Trick

Effective Cost Price (CP) = 14360 + 240 = 14600.

To get a Profit of 15%, multiplier = (100 + 15) ÷ 100 = 1.15.

Selling Price (SP) = 14600 × 1.15.

Calculation: 14600 × (1 + 0.15) = 14600 + 2190 = 16790.

∴ The correct answer is Rs. 16,790.

Alternate Method

Given: Purchase Price = Rs. 14,360, Overhead Expenses = Rs. 240, Profit Percentage = 15%. Formulas: Total CP = Purchase Price + Overhead Expenses | SP = CP × (100 + Profit%) ÷ 100

Steps: ⇒ Total Cost Price (CP) = 14360 + 240 = 14,600 ⇒ Profit Amount = 15% of 14,600 = (15 ÷ 100) × 14600 ⇒ Profit Amount = 15 × 146 = 2,190 ⇒ Selling Price (SP) = Total CP + Profit = 14600 + 2190 ⇒ Selling Price (SP) = 16,790

∴ The correct answer is Rs. 16,790.

Additional Information

Effective Cost Price

Any additional expenditure incurred on an article like transportation, repairs, or labor after buying is added to the Cost Price to find the effective CP.

Profit and Loss Basic

Profit is always calculated on the Cost Price (CP) unless stated otherwise. If SP > CP, it is Profit. If CP > SP, it is Loss.

Shortcut Trick

Total Work = LCM(24, 8) = 24 units.

Efficiency of (P+Q) = 24 ÷ 24 = 1 unit/day.

Efficiency of (R+S) = 24 ÷ 8 = 3 units/day.

Combined Efficiency = 1 + 3 = 4 units/day.

Time together = 24 ÷ 4 = 6 days.

∴ The correct answer is 6 days.

Alternate Method

Given: Time for (P+Q) = 24 days, Time for (R+S) = 8 days.

Formula: Total Work = Efficiency × Time

⇒ Total Work = LCM of (24, 8) = 24 units.

⇒ Efficiency of (P + Q) = 24 ÷ 24 = 1 unit/day.

⇒ Efficiency of (R + S) = 24 ÷ 8 = 3 units/day.

⇒ Total combined efficiency of (P + Q + R + S) = 1 + 3 = 4 units/day.

⇒ Days taken together = Total Work ÷ Combined Efficiency

⇒ Required Days = 24 ÷ 4 = 6 days.

∴ The correct answer is 6 days.

Additional Information

Work and Efficiency Relation

Efficiency is inversely proportional to the time taken to complete a work. If A takes x days and B takes y days, the ratio of their efficiencies is y : x.

Combined Work Formula

If two groups A and B take x and y days respectively, they together take (x × y) ÷ (x + y) days to finish the work.

Work and Wages

Wages are always distributed in the ratio of the total work done by each individual or group (or efficiency ratio if they work for the same duration).

Shortcut Trick

Radius (r) = 30 ÷ 2 = 15 m, Height (h) = 8 m.

Using the Pythagorean triplet (8, 15, 17), the slant height (l) = 17 m.

Canvas required = Curved Surface Area = πrl

⇒ Area = 3.14 × 15 × 17 = 3.14 × 255 = 800.7

∴ The correct answer is 800.7 m².

Alternate Method

Given:

Diameter of the base of the cone (d) = 30 m

⇒ Radius (r) = d ÷ 2 = 30 ÷ 2 = 15 m

Height of the cone (h) = 8 m

Value of π = 3.14

h = 8 m

r = 15 m l = 17 m Canvas Area = Curved Surface Area

Formula Used:

Slant height of a cone (l) = √(r² + h²)

Curved Surface Area (CSA) of a cone = πrl

Calculations:

⇒ First, find the slant height (l) of the conical heap:

⇒ l = √(15² + 8²)

⇒ l = √(225 + 64)

⇒ l = √289 = 17 m

⇒ The area of the canvas required to just cover the heap is equal to its Curved Surface Area.

⇒ Canvas required = πrl

⇒ Canvas required = 3.14 × 15 × 17

⇒ Canvas required = 3.14 × 255

⇒ Canvas required = 800.7 m²

∴ The correct answer is 800.7 m².

Additional Information

Total Surface Area of a Cone

The total surface area includes both the curved surface and the flat circular base: TSA = πrl + πr² = πr(l + r).

Volume of a Cone

The volume of a cone is exactly one-third the volume of a cylinder that has the same base radius and height: Volume = (1/3)πr²h.

Pythagorean Triplets

Using standard right-angle triangle triplets such as (3, 4, 5), (5, 12, 13), and (8, 15, 17) helps in quickly finding the missing side lengths in 2D and 3D geometry problems.

Given:

Simple interest = Rs. 3720

Time (T) = 3 years

Rate (R) = 8%

Concept:

Simple interest is the interest calculated on the principal portion of the loan or the original contribution to the saving account.

Formula Used:

Simple Interest = (P × R × T)/100

Calculation: 

Let the principal be 'P' 

Simple Interest = (P × R × T)/100

⇒ 3720 = (P × 8 × 3)/(100)

⇒ 3720 = 24P/100

⇒ P = 372000 ÷ 24

⇒ P = Rs. 15500

∴ The principal or the amount borrowed from the bank is Rs. 15500.

Shortcut Trick

Radius (r) = 42 cm.

Curved Surface Area (CSA) of a hemisphere = 2πr².

Half of CSA = (1/2) × 2πr² = πr².

Calculation: (22/7) × 42 × 42 = 22 × 6 × 42 = 132 × 42 = 5544 cm².

∴ The correct answer is 5544 cm².

Alternate Method

Given:

Radius (r) of the hemisphere = 42 cm.

Value of π = 22/7.

Formula Used:

Curved Surface Area (CSA) of a hemisphere = 2πr²

Required Value = (1/2) × CSA = πr²

Calculations:

⇒ Required Area = π × r × r

⇒ Required Area = (22/7) × 42 × 42

⇒ Required Area = 22 × (42 ÷ 7) × 42

⇒ Required Area = 22 × 6 × 42

⇒ Required Area = 132 × 42

⇒ Required Area = 5544 cm²

∴ The correct answer is 5544 cm².

Additional Information

Total Surface Area of Hemisphere

The Total Surface Area (TSA) includes the curved part and the flat circular base: TSA = 3πr².

Volume of Hemisphere

The Volume of a hemisphere is exactly half the volume of a sphere: V = (2/3)πr³.

Sphere Properties

For a complete Sphere, the Surface Area is 4πr² and the Volume is (4/3)πr³.

Given:

Time taken by A = 20 days

Time taken by B = 30 days

Formula used:

Efficiecy = Total work/Number of days

Calculation:

LCM of 20 and 30 = 60

Efficiency of A = 60/20 = 3

Efficiency of B = 60/30 = 2

Combined efficiency = 2 + 3 = 5

Work done by B alone = 7.5 × 2 = 15

Remaining work = 60 – 15 = 45

∴ Number of days they worked together = 45/5 = 9 days

Given:

A manufactures wheat in 30% of land

B manufactures rice in 25% of land

C manufactures Lady finger in 20% of land

D manufactures cotton in 15% of land

E manufactures potato in 10% of land.

Calculation:

Total land owned by C after B sells his part of land = (25 + 20)% of 400

⇒ Total land owned by C = 45% of 400

⇒ Total land owned by C = 0.45 × 400

⇒ Total land owned by C = 180 acres

∴ Total land owned by C is 180 acres

Given:

A manufactures wheat in 30% of land

B manufactures rice in 25% of land

C manufactures Lady finger in 20% of land

D manufactures cotton in 15% of land

E manufactures potato in 10% of land.

Calculation:

A manufactures wheat in 30% of land = 0.30 × 400

⇒ E manufactures potato in 10% of land = 0.10 × 400

⇒ Wheat + Potato = 120 + 40

⇒ Land on which wheat and potato is produced = 160 acres

Given:

A manufactures wheat in 30% of land

B manufactures rice in 25% of land

C manufactures Lady finger in 20% of land

D manufactures cotton in 15% of land

E manufactures potato in 10% of land.

Formula used:

Total produce = Number of acres owned × Produce per acre

Calculation:

D manufactures cotton in 15% of land

⇒ Land owned by D = 0.15 × 400

⇒ Land owned by D = 60 acres

∴ land owned by D is 60 acres

Given:

Price of 1 kg of wheat is increased by 50 percent and the increase is of Rs. 25.

Concept:

To find the new price, we need to calculate the original price first using the percentage increase, then add the increase to the original price.

Formula Used:

Percentage Increase = (Increase / Original Price) × 100

Calculation:

⇒ Let the original price of 1 kg of wheat be Rs. x.

⇒ 50% of x = 25

⇒ (50 / 100) × x = 25

⇒ 0.5x = 25

⇒ x = 25 / 0.5

⇒ x = 50

⇒ New Price = Original Price + Increase

⇒ New Price = 50 + 25

⇒ New Price = 75

∴ The new price of the wheat per kg is Rs. 75.