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Total number of cars sold = 40500 × (360/90) = 162000

Difference in numbers of cars of E and A sold = (75 - 45)/360 × 162000 = 13500

Total number of cars sold = 40500 × (360/90) = 162000

Ratio between the number of cars sold of model D and E = 90/75 = 6 : 5

Total number of cars sold = 72900 × (360/90) = 291600

Given : 

Susan can type 12 pages in 6 minutes.

Mary can type 6 pages in 12 minutes. 

Formula Used : 

Work Done = Time × Efficiency

Calculation : 

Efficiency of Susan = 2

Efficiency of Mary = 0.5

No of pages = (2 + 0.5) × 32 min 

⇒ 2.5 × 32 min

⇒ 25/10 × 32 min

⇒ 80

∴ The correct answer is 80.

Shortcut Trick

Let the Marked Price (MP) be 100.

Successive discount multiplier = (1 − 10÷100) × (1 − 12÷100) × (1 − 15÷100)

⇒ 0.90 × 0.88 × 0.85 = 0.6732

Selling Price (SP) = 100 × 0.6732 = 67.32

Single Equivalent Discount = 100 − 67.32 = 32.68%

∴ The correct answer is 32.68%.

Alternate Method

Given → Discounts: d₁ = 10%, d₂ = 12%, d₃ = 15%. Formulas: Successive Discount = a + b − (a × b) ÷ 100

⇒ Step 1: Combine 10% and 12% ⇒ 10 + 12 − (10 × 12) ÷ 100 = 22 − 1.2 = 20.8% ⇒ Step 2: Combine 20.8% and 15% ⇒ 20.8 + 15 − (20.8 × 15) ÷ 100 ⇒ 35.8 − (312 ÷ 100) = 35.8 − 3.12 ⇒ 32.68%

∴ The correct answer is 32.68%.

Additional Information

Successive Discount Concept

When multiple discounts are applied, each subsequent discount is calculated on the reduced price. The order of discounts does not change the final result.

Fraction Method

10% = 1/10 (10→9), 12% = 3/25 (25→22), 15% = 3/20 (20→17). Multiply ratios: (10×25×20) : (9×22×17) = 5000 : 3366. Discount = (1634/5000) × 100 = 32.68%.

Concept use:

To calculate the new salary after a percentage increase, we can use the formula:

New Salary = Old Salary + (Old Salary x Percentage Increase)

Where:

Old Salary = Rs. 50,000

Percentage Increase = 10% (or 0.10 in decimal form)

Calculation:

New Salary = 50,000 + (50,000 x 0.10)

New Salary = 50,000 + 5,000

New Salary = Rs. 55,000

Hence, the new salary after a 10% increase is Rs. 55,000.

Given:

A can do the work in 10 days

B can do the work in 15 days

C can do the work in 20 days

Formula used:

Work done = Time taken × Efficiency

Time taken ∝ 1/Efficiency

Calculation:

1^st day work by A = 1/10

2^nd day work by B = 1/15

3^rd day work by  C = 1/20

Total work completed in 3 days

⇒ 1/10 + 1/15 + 1/20

⇒ (6 + 4 + 3)/60 = 13/60

Time taken to complete the work

⇒ 60/13

⇒ 4(8/13)

They finish the same work in 4(8/13) days.

Work done together in 1 day is:

⇒ 6 + 4 + 3 = 13

Total time required to complete the work ⇒ 60/13

⇒ \(4\frac{8}{13}\) days

Shortcut Trick

Interest difference % = (11 years − 6 years) × 4% = 5 × 4% = 20%.

Given that 20% of the Amount (Principal) = ₹7,500.

Total Amount (100%) = 7,500 × (100 ÷ 20) = 7,500 × 5 = ₹37,500.

∴ The correct answer is ₹37,500.

Alternate Method

Given: Rate (R) = 4% p.a., Time₁ (T₁) = 6 years, Time₂ (T₂) = 11 years, SI difference = ₹7,500.

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

⇒ SI₂ − SI₁ = 7500

⇒ [(P × 4 × 11) ÷ 100] − [(P × 4 × 6) ÷ 100] = 7500

⇒ (44P ÷ 100) − (24P ÷ 100) = 7500

⇒ 20P ÷ 100 = 7500

⇒ P ÷ 5 = 7500

⇒ P = 7500 × 5

⇒ P = 37500

∴ The correct answer is ₹37,500.

Additional Information

Simple Interest Concept

Simple interest is calculated only on the Principal amount for the entire duration. Formula: SI = P × R × T ÷ 100.

Direct Proportionality

When Principal (P) and Rate (R) are constant, the Simple Interest is directly proportional to the Time (T). Doubling the time doubles the interest.

Total Amount (Maturity)

The total amount (A) after T years is the sum of Principal and Interest: A = P + SI = P[1 + (RT ÷ 100)].

Given:

length of the longest rod placed in it = 12√3 m.

Formula used:

Diagonal of cube = a√3

Area of floor = a²

Calculation Used:

Length of the longest rod of cube = Diagonal of cube = \(√ {3{a^2}} ;;;;\)

⇒ 12√3 = a√3

⇒ a = 12 m

Area of floor = a2

⇒ Area of floor = 12²  = 144 m².

∴ The area of the floor is 144 m².

Shortcut Trick

For quarterly compounding, the Time is 1 period (3 months = 1 quarter).

Rate for 1 quarter = 5% ÷ 4 = 1.25%.

Compound Interest = 1.25% of ₹ 8,000.

⇒ 8000 × (1.25/100) = 80 × 1.25 = ₹ 100.

∴ The correct answer is ₹ 100.

Alternate Method

Given:

Principal (P) = ₹ 8,000

Rate (R) = 5% per annum

Time (T) = 3 months

Formula Used:

For quarterly compounding: Rate (r) = R/4 and n = T(in years) × 4

Amount (A) = P(1 + r/100)ⁿ

Calculations:

⇒ r = 5/4 = 1.25%

⇒ n = (3/12) × 4 = 1 quarter

⇒ A = 8000 × (1 + 1.25/100)¹

⇒ A = 8000 × (101.25/100)

⇒ A = 80 × 101.25 = ₹ 8,100

⇒ Compound Interest (CI) = A − P

⇒ CI = 8100 − 8000 = ₹ 100

∴ The correct answer is ₹ 100.

Additional Information

Quarterly Compounding Rule

When interest is compounded quarterly, the annual rate is divided by 4 and the number of years is multiplied by 4.

Half-Yearly Compounding

When interest is compounded half-yearly, the annual rate is divided by 2 and the time in years is multiplied by 2.

CI for 1^st Period

For the very first compounding period, the Simple Interest and Compound Interest are always equal.