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Shortcut Trick

Loss 20% → Selling Price (SP₁) is 80% of Cost Price (CP).

₹612 represents 80%.

New SP (₹918) represents (80 ÷ 612) × 918.

⇒ (80 ÷ 2) × 3 = 120%.

Profit = 120% − 100% = 20% or 0.2.

∴ The correct answer is 0.2.

Alternate Method

Given: SP₁ = ₹612, Loss = 20%, SP₂ = ₹918

Formula: CP = SP × 100 ÷ (100 − Loss%)

SP1: ₹612

CP: ₹765

SP2: ₹918

20% Loss

Profit %?

⇒ CP = 612 × 100 ÷ (100 − 20)

⇒ CP = 612 × 100 ÷ 80 = 612 × 1.25 = ₹765

⇒ Profit = SP₂ − CP = 918 − 765 = ₹153

⇒ Profit % = (Profit ÷ CP) × 100 = (153 ÷ 765) × 100

⇒ Profit % = 1/5 × 100 = 20%

⇒ In decimal form, 20% = 0.2

∴ The correct answer is 0.2.

Additional Information

Profit and Loss Formulas

Profit % = (Profit ÷ CP) × 100 and Loss % = (Loss ÷ CP) × 100. Profit or Loss is always calculated on the Cost Price unless specified.

Decimal Representation of Percentages

To convert percentage to decimal, divide by 100 (e.g., 20% = 20/100 = 0.2). To convert decimal to percentage, multiply by 100.

Marked Price and Discount

SP = MP − Discount. Discount % = (Discount ÷ MP) × 100. Marked Price is the price listed on the product.

Shortcut Trick

Sum of Length and Breadth = Semi-perimeter = 90 ÷ 2 = 45 m.

Ratio sum (5 + 4) = 9 units.

9 units = 45 m → 1 unit = 5 m.

Breadth = 4 units = 4 × 5 = 20 m.

∴ The correct answer is 20 m.

Alternate Method

Given:

Ratio of Length (L) to Breadth (B) = 5 : 4

Perimeter of the rectangular field = 90 m

Formula Used:

Perimeter of a rectangle = 2 × (Length + Breadth)

Length (L) = 5x Breadth (B) = 4x Perimeter = 90 m Breadth = 4 × 5 = 20 m

Calculations:

⇒ Let Length = 5x and Breadth = 4x

⇒ 2 × (5x + 4x) = 90

⇒ 2 × 9x = 90

⇒ 18x = 90

⇒ x = 90 ÷ 18 = 5

⇒ Breadth = 4x = 4 × 5 = 20 m

∴ The correct answer is 20 m.

Additional Information

Area of Rectangle

The total space occupied by the rectangle is calculated as Area = Length × Breadth.

Diagonal of Rectangle

The distance between opposite corners is given by the Pythagorean theorem: Diagonal = √(Length² + Breadth²).

Perimeter of a Square

If the length and breadth are equal (side a), the perimeter is given by P = 4 × a.

Shortcut Trick

Assumed average of 30 girls = 13 years.

Deviation for 18 girls = (15 − 13) = +2 years each.

Total surplus age = 18 × 2 = +36 years.

This surplus must be balanced by the remaining 12 girls: −36 ÷ 12 = −3 years per girl.

Average age of 12 girls = 13 − 3 = 10 years.

∴ The correct answer is 10 years.

Alternate Method

Given:

Total girls (n_total) = 30, Total Average (A_total) = 13

Group 1 (n₁) = 18, Average 1 (A₁) = 15

Remaining (n₂) = 30 − 18 = 12

Formula Used: Total Sum = Number of girls × Average age

18 Girls (15 yrs) 12 Girls (?)

Total: 30 Girls (Avg = 13 yrs) Sum = 30 × 13 = 390 years

⇒ Total age of 30 girls = 30 × 13 = 390 years

⇒ Total age of 18 girls = 18 × 15 = 270 years

⇒ Total age of remaining 12 girls = 390 − 270 = 120 years

⇒ Average age of remaining 12 girls = 120 ÷ 12 = 10 years

∴ The correct answer is 10 years.

Additional Information

Weighted Average Formula

When a group is divided into two parts, the combined average is given by A = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Net Deviation Rule

The sum of deviations of all observations from their arithmetic mean is always zero. This is used for faster balancing in grouping problems.

Effect of Change in Values

If each observation is increased, decreased, multiplied, or divided by a constant 'k', the average also changes by the same operation 'k'.

Shortcut Trick

Ratio of A : B = 80 : 100 = 4 : 5

B as a percentage of A = (B / A) × 100

Required percentage = (5 / 4) × 100 = 125%

∴ The correct answer is 125%.

Alternate Method

Given:

A’s salary = 80% of B’s salary

Formula Used:

Percentage = (Value / Base Value) × 100

B's Salary (100 units)

A's Salary (80 units)

B/A × 100 = (100/80) × 100 = 125%

Calculations:

⇒ Let B’s salary = ₹100

⇒ A’s salary = 80% of 100 = ₹80

⇒ Required Percentage = (B’s Salary / A’s Salary) × 100

⇒ Required Percentage = (100 / 80) × 100

⇒ Required Percentage = (5 / 4) × 100

⇒ Required Percentage = 125%

∴ The correct answer is 125%.

Additional Information

Percentage to Fraction Conversion

To convert a percentage to a fraction, divide by 100. Example: 80% = 80/100 = 4/5. 125% = 125/100 = 5/4.

Reciprocal Percentages

If A is x% of B, then B is (100 × 100 / x)% of A. Here, 10000 / 80 = 125%.

Percentage Change

Percentage Increase/Decrease = (Difference / Original Value) × 100. Useful when comparing salary hikes or reductions.

Shortcut Trick Profit = 20% = 1/5 (Ratio of Profit to CP) Ratio of CP : SP = 5 : (5 + 1) = 5 : 6 6 units = ₹540 1 unit = 540 ÷ 6 = 90 5 units = 5 × 90 = 450 ∴ The correct answer is ₹450. Alternate Method Given: Selling Price (SP) = ₹540, Profit Percentage = 20% Formula: CP = [SP ÷ (100 + Profit%)] × 100

Cost Price (100%) +20%

Sale Price = ₹540 (120%)

Base CP Value

⇒ CP = [540 ÷ (100 + 20)] × 100 ⇒ CP = [540 ÷ 120] × 100 ⇒ CP = 4.5 × 100 ⇒ CP = ₹450 ∴ The correct answer is ₹450. Additional Information Profit and Loss Basics Profit occurs when SP > CP. Profit = SP − CP. Profit% is always calculated on the CP: (Profit ÷ CP) × 100. Loss Percentage Formula When SP < CP, Loss = CP − SP. Loss% = (Loss ÷ CP) × 100. Similarly, CP = [SP ÷ (100 − Loss%)] × 100. Successive Discounts If two discounts d1 and d2 are given, the effective discount = d1 + d2 − (d1 × d2) ÷ 100.

The correct answer is 'inappropriate'.

Key Points

• The word "incongruous" means not in harmony or keeping with the surroundings or other aspects of something. In this sentence, the author is saying that traditional methods seem out of place or inappropriate in our technical age.
• The most appropriate option that is nearest in meaning to "incongruous" is "inappropriate".
• The other options - "unswerving," "constant," and "unvarying" - do not accurately convey the meaning of "incongruous".
• They all refer to something that is consistent or unchanging, which is not the same as being out of place or inappropriate.
• Therefore, the best answer is "inappropriate", as it captures the sense of something being unsuitable or not fitting in with its surroundings or context.

The correct answer is: Frivolous

Key Points

• Grave often refers to something serious, solemn, or giving cause for concern. (गंभीर)
• Example: The news about the pandemic had a grave impact on the community.
• Marked option Frivolous describes something lacking in seriousness or importance, often characterized by a lack of depth or relevance. (तुच्छ)
• Example: While discussing important issues, she dismissed the conversation as frivolous and unimportant.
• So, the most appropriate antonym for 'Grave' is 'Frivolous'.

Therefore, the correct answer is option 2.

Additional Information

• Native refers to something or someone that is originally from a particular place or region. (देशी)
• Foreign describes something or someone that is not from one's own country or locality; it is of external origin. (विदेशी)
• Serious describes something that is earnest, important, or not to be taken lightly. (महत्वपूर्ण)

The correct answer is 'To face the risk' (Option 1).

 Key Points

• "To bell the cat" is an idiom that originated from an old fable. It means to face or undertake a dangerous or risky task.
• According to the fable, the mice decided to put a bell on a cat, so they would know when it was coming. However, one wise mouse asked who would put the bell on the cat. So the phrase has come to signify a significant and risky, but necessary task.
• The other options - "Conflict", "Make friendship", and "Facing enemy" - do not accurately capture the meaning of this phrase.

Therefore, the correct answer is Option 1.

 Additional Information

• The phrase "to bell the cat" highlights how often times it's easy to propose solutions, but executing them, especially when risks are involved, is much more challenging.

The correct answer is 'Option 4, Regicide'.

Key Points

• The expression "the murder of the king" describes an act of killing a king. In English, this act is referred to as 'Regicide'. In Hindi, it is referred to as 'Rajyahan' (राज्यहन).
• Example: The monarch's reign ended with regicide.
• 'Regicide' refers to the act of killing a king. In Hindi, it's called 'Rajyahan' (राज्यहन).
• Example: The history book covered the infamous regicide that plunged the country into chaos.

Therefore, the correct answer is 'Option 4, Regicide'.

Additional Information

• 'Suicide' (आत्महत्या) is the act of intentionally causing one's own death.
• 'Fratricide' (भाईवध) refers to the act of killing one's brother.
• 'Homicide' (नरहत्या) is the act of one human killing another.

The erroneous spelling is "premitivism".

Key Points

• Let's look at the correct spelling and meaning of the word:
• Primitivism: a belief in the value of what is simple and unsophisticated, expressed as a philosophy of life or through art or literature.
• ​Example: Primitivism was a key inspiration for a lot of painting schools such as cubism, fauvism and post-impressionism.

​Hence, the correct answer is option 2.

Additional Information

• Let's look at the meaning of the other words.
• ​radicalism: the beliefs or actions of people who advocate thorough or complete political or social reform.
• raged: feel or express violent uncontrollable anger.
• debates: an argument about a particular subject, especially one in which many people are involved.
• ​All the other words are spelled correctly.​