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Shortcut Trick

Order quantity 22 exceeds the 20 sweater limit, so the 25% discount is applicable.

Net Selling Price (SP) of one sweater = 75% of ₹600 = ₹450.

Total amount paid for 22 sweaters = 22 × 450 = ₹9,900.

∴ The correct answer is ₹9,900.

Alternate Method

Given:

Marked Price (MP) of 1 sweater = ₹600

Quantity ordered = 22 sweaters

Discount for > 20 sweaters = 25%

Formula Used:

Selling Price (SP) = MP − Discount

Total Amount = SP per unit × Quantity

Calculations:

⇒ Total MP of 22 sweaters = 22 × 600 = ₹13,200

⇒ Since 22 > 20, Discount rate = 25%

⇒ Total Discount amount = 25% of ₹13,200

⇒ Total Discount = (25 ÷ 100) × 13,200 = ₹3,300

⇒ Amount paid by retailer = Total MP − Total Discount

⇒ Amount paid = 13,200 − 3,300 = ₹9,900

∴ The correct answer is ₹9,900.

Additional Information

Marked Price (List Price)

The price mentioned on the product tag. Discount is always calculated on this value: SP = MP × (100 − D%)/100.

Successive Discount

If two discounts d₁% and d₂% are given, the effective discount is [d₁ + d₂ − (d₁ × d₂)/100]%.

Profit and Loss Relation

The relationship between MP and CP is given by: MP/CP = (100 + P%) / (100 − D%), where P is profit % and D is discount %.

Shortcut Trick

Net increase in daily riders = 4,860 − 4,500 = 360.

Percentage growth = (Change ÷ Initial Value) × 100.

Growth % = (360 ÷ 4,500) × 100 = 360 ÷ 45 = 8%.

∴ The correct answer is 8%.

Alternate Method

Given:

Average riders last month (Initial Value) = 4,500

Average riders this month (Final Value) = 4,860

Formula Used:

Percentage Increase = [(Final Value − Initial Value) ÷ Initial Value] × 100

Calculations:

⇒ Absolute increase = 4,860 − 4,500 = 360

⇒ Percentage growth = (360 ÷ 4,500) × 100

⇒ Percentage growth = (360 ÷ 45)

⇒ Percentage growth = 8%

∴ The correct answer is 8%.

Additional Information

Percentage Change Rule

Always use the initial or original value as the denominator (base) when calculating percentage growth or percentage reduction.

Multiplying Factor

An 8% increase is equivalent to multiplying the original value by (1 + 8/100) = 1.08. Thus, 4,500 × 1.08 = 4,860.

Fraction to Percentage

The ratio 360/4,500 simplifies to 36/450 = 4/50 = 2/25. Since 1/25 = 4%, then 2/25 = 8%.

Shortcut Trick

Total Surface Area (TSA) = 2 × 22/7 × 14 × (14 + 10) = 2112 cm².

Since 20% is blue, the remaining red portion is 80%.

Red Area = 80% of 2112 = 0.8 × 2112 = 1689.6 cm².

∴ The correct answer is 1689.6 cm².

Alternate Method

Given:

Radius (r) = 14 cm

Height (h) = 10 cm

Formula Used:

Total Surface Area (TSA) of a closed cylindrical reservoir = 2πr(r + h)

Calculations:

⇒ Total Surface Area = 2 × (22/7) × 14 × (14 + 10)

⇒ TSA = 2 × 22 × 2 × 24

⇒ TSA = 44 × 48 = 2112 cm²

⇒ Area coated in blue paint = 20% of 2112 = 422.4 cm²

⇒ Area coated in red paint = Total Area − Blue Area

⇒ Red Area = 2112 − 422.4 = 1689.6 cm²

∴ The correct answer is 1689.6 cm².

Additional Information

Curved Surface Area (CSA)

The lateral area of a cylinder excluding the top and bottom circles is 2πrh.

Volume of a Cylinder

The total capacity or space enclosed by a cylinder is given by πr²h.

Open Cylinder TSA

If a cylinder is open at one end, the surface area is πr² + 2πrh = πr(r + 2h).

Shortcut Trick

Effective Selling Price (SP) per 1 kg displayed = 60 × 1.20 × 0.90 = ₹64.80.

Actual Cost Price (CP) for 900 g given = (60 ÷ 1000) × 900 = ₹54.

Profit on each transaction = 64.80 − 54 = ₹10.80.

∴ The correct answer is ₹10.80.

Alternate Method

Given:

Cost Price (CP) of rice = ₹60 per kg

Mark-up percentage = 20%

Discount percentage = 10%

Faulty weight = 900 g instead of 1000 g

Step-by-step Calculation:

⇒ Cost Price (CP) of 1000 g = ₹60

⇒ Marked Price (MP) = 60 + (20% of 60) = 60 + 12 = ₹72

⇒ Selling Price (SP) = 72 − (10% of 72) = 72 − 7.20 = ₹64.80

⇒ Since the shopkeeper gives only 900 g when the buyer pays for 1 kg, we must find the cost of the actual quantity sold.

⇒ Actual CP for 900 g = (60 ÷ 1000) × 900 = ₹54

⇒ Profit = Selling Price − Actual Cost Price

⇒ Profit = 64.80 − 54 = ₹10.80

∴ The correct answer is ₹10.80.

Additional Information

Dishonest Dealer Concept

Profit occurs in two ways: by increasing the price (markup) and by reducing the weight given. Net Profit % = [ (True weight − False weight) / False weight ] × 100 (when sold at CP).

Successive Percentage Change

If a value is increased by x% and then decreased by y%, the effective change is [ x − y − (xy/100) ] %.

Relationship between CP, MP, and SP

MP = CP × (100 + Mark-up%)/100 and SP = MP × (100 − Discount%)/100.

Shortcut Trick

To find the larger value (Mary) when the sum and difference of two quantities are known:

Mary's age = (Combined Sum + Age Difference) ÷ 2

Mary's age = (27 + 3) ÷ 2 = 30 ÷ 2 = 15 years.

∴ The correct answer is 15 years.

Alternate Method

Given:

Combined age of Mary and Sister = 27 years

Difference in their ages = 3 years

Calculation:

Let the age of Mary's sister be x years.

⇒ Mary's age = x + 3

⇒ Total combined age = x + (x + 3) = 27

⇒ 2x + 3 = 27

⇒ 2x = 27 − 3

⇒ 2x = 24

⇒ x = 24 ÷ 2 = 12 years (Sister's age)

⇒ Mary's age = 12 + 3 = 15 years.

∴ The correct answer is 15 years.

Additional Information

Sum and Difference Formula

If the sum of two numbers is S and their difference is D, then the larger number is (S + D) ÷ 2 and the smaller number is (S − D) ÷ 2.

Constant Age Difference

The age difference between two individuals remains constant throughout their lives; it does not change as they grow older.

Ratio Method for Ages

If ages are given in a ratio a:b, the difference between the ratio parts corresponds directly to the numerical age difference.

Shortcut Trick

Solve the nested radical from the innermost part: √(419 + 157) = √576 = 24.

Proceed to the next layer: √(3225 + 24) = √3249 = 57.

Solve the final outer layer: √(1624 + 57) = √1681 = 41.

Shortcut logic: The result of √(1624 + x) must be slightly more than √1624 ≈ 40.3. Among the options, 41 is the only possible integer.

∴ The correct answer is 41.

Alternate Method

Given Expression: √(1624 + √(3225 + √(419 + 157)))

Simplification Steps:

⇒ First, add the innermost numbers: 419 + 157 = 576

⇒ √(1624 + √(3225 + √576))

⇒ Since √576 = 24:

⇒ √(1624 + √(3225 + 24))

⇒ Add the values inside the next root: 3225 + 24 = 3249

⇒ √(1624 + √3249)

⇒ Since √3249 = 57 (as 50² = 2500 and 60² = 3600):

⇒ √(1624 + 57)

⇒ Add the remaining values: 1624 + 57 = 1681

⇒ √1681

⇒ 41

∴ The correct answer is 41.

Additional Information

Square Root Properties

For a number ending in 1, its square root ends in either 1 or 9. Since 41² = 1681 and 49² = 2401, 41 is the correct root for 1681.

Perfect Square Identification

A perfect square never ends with the digits 2, 3, 7, or 8. This helps in quickly eliminating incorrect results during multi-step simplification.

Nested Radicals

Always solve nested radicals from inside-out. Simplification of the innermost root provides a whole number that completes the next perfect square.

Shortcut Trick

Ratio of Officers to Clerks = 10 : 30 = 1 : 3

Assume base average = ₹25,000 (lower value)

Extra from 1 Officer = 45,000 − 25,000 = ₹20,000

Distribute this extra among total parts (1 + 3 = 4): 20,000 ÷ 4 = ₹5,000

Net Average = 25,000 + 5,000 = ₹30,000

∴ The correct answer is ₹30,000.

Alternate Method

Given:

Number of officers = 10 | Average salary of officers = ₹45,000

Number of clerks = 30 | Average salary of clerks = ₹25,000

Formula: Average = (Total Salary of all staff) ÷ (Total number of staff)

⇒ Total salary of 10 officers = 10 × 45,000 = ₹4,50,000

⇒ Total salary of 30 clerks = 30 × 25,000 = ₹7,50,000

⇒ Total salary of entire staff = 4,50,000 + 7,50,000 = ₹12,00,000

⇒ Total number of staff members = 10 + 30 = 40

⇒ Average salary of staff = 12,00,000 ÷ 40

⇒ Average salary = ₹30,000

∴ The correct answer is ₹30,000.

Additional Information

Weighted Average Formula

When two groups are combined, the combined average A is given by (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Alligation Rule

The ratio of the number of items in two groups is (A₂ − A_mix) : (A_mix − A₁), where A_mix is the average of the combined group.

Average Property

The combined average always lies between the lowest and the highest individual averages of the constituent groups.

Shortcut Trick

Ratio of E : F : G : H = 9 : 7 : 5 : 3

Difference between F and G units = 7 − 5 = 2 units

Given, 2 units = ₹4000 ⇒ 1 unit = ₹2000

E's share = 9 units = 9 × 2000 = ₹18000

∴ The correct answer is ₹18000.

Alternate Method

Given:

Ratio of distribution among E, F, G, H = 9 : 7 : 5 : 3

Difference between share of G and F = ₹4000

Formula Used:

Value of one unit = Difference in values ÷ Difference in ratio units

Individual share = Ratio unit × Value of one unit

Calculations:

⇒ Let the amounts received by E, F, G, and H be 9x, 7x, 5x, and 3x.

⇒ According to the question, F − G = 4000

⇒ 7x − 5x = 4000

⇒ 2x = 4000

⇒ x = 4000 ÷ 2 = 2000

⇒ Share of E = 9x = 9 × 2000

⇒ Share of E = ₹18000

∴ The correct answer is ₹18000.

Additional Information

Ratio Equality

A ratio remains unchanged if both terms are multiplied or divided by the same non-zero number (e.g., a:b = ak:bk).

Proportional Distribution

To divide a total amount T in the ratio a:b:c, the first part is [a / (a+b+c)] × T.

Compound Ratio

For two ratios a:b and c:d, the compounded ratio is (ac) : (bd).

Given:

Expression = 3.46 + 3 1/4 − 5 1/8 + 4.25 + 0.165

Formula used:

Conversion of mixed fractions to decimal form and BODMAS rule for basic arithmetic.

Calculations:

First, convert the mixed fractions into decimals:

⇒ 3 1/4 = 3 + 0.25 = 3.25

⇒ 5 1/8 = 5 + 0.125 = 5.125

Now, substitute these values into the given expression:

⇒ 3.46 + 3.25 − 5.125 + 4.25 + 0.165

Group the positive terms together to simplify the addition:

⇒ (3.46 + 3.25 + 4.25 + 0.165) − 5.125

⇒ 11.125 − 5.125

⇒ 6

∴ The correct answer is option (2).

Shortcut Trick

Ratio of Amount (A) to Principal (P) = 21218 : 20000

Divide both sides by 2 to get perfect squares: 10609 : 10000

Since the time is 2 years, take the square root: √10609 : √10000 = 103 : 100

Rate of Interest = (103 − 100) / 100 × 100 = 3%

∴ The correct answer is 3%.

Alternate Method

Given:

Principal (P) = ₹20,000

Amount (A) = ₹21,218

Time (n) = 2 years

Formula Used:

A = P(1 + r/100)ⁿ

Calculations:

⇒ 21218 = 20000(1 + r/100)²

⇒ 21218 ÷ 20000 = (1 + r/100)²

⇒ 10609 ÷ 10000 = (1 + r/100)²

⇒ (103/100)² = (1 + r/100)²

⇒ 103/100 = 1 + r/100

⇒ 1.03 = 1 + r/100

⇒ r/100 = 1.03 − 1 = 0.03

⇒ r = 0.03 × 100 = 3

∴ The correct answer is 3%.

Additional Information

Effective Rate of Interest

For 2 years at r% compound interest, the effective rate is given by R_eff = r + r + (r × r)/100.

Difference between CI and SI

The difference between Compound Interest and Simple Interest for 2 years is P × (r/100)².

Rule of 72

A quick way to estimate how long it takes for an investment to double is dividing 72 by the annual rate of interest (t ≈ 72/r).