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Shortcut Trick

Let total work be the LCM of 14 and 42 = 42 units.

Combined efficiency of A and B = 42 ÷ 14 = 3 units/day.

Efficiency of A alone = 42 ÷ 42 = 1 unit/day.

Efficiency of B alone = 3 − 1 = 2 units/day.

Time taken by B for one-third work = (42 ÷ 3) ÷ 2 = 14 ÷ 2 = 7 days.

∴ The correct answer is 7 days.

Alternate Method

Given:

Time taken by A and B to complete the work = 14 days

Time taken by A alone to complete the work = 42 days

Calculations:

⇒ Efficiency of B = Efficiency of (A + B) − Efficiency of A

⇒ Efficiency of B = 3 − 1 = 2 units/day

⇒ Target work for B = 1/3 of Total Work

⇒ Target work = (1 ÷ 3) × 42 = 14 units

⇒ Time taken by B = Target work ÷ Efficiency of B

⇒ Time taken by B = 14 ÷ 2 = 7 days

∴ The correct answer is 7 days.

Additional Information

Pipes & Cisterns

Works exactly like Time & Work problems. An inlet pipe has a positive efficiency (filling), while an outlet pipe or a leak has a negative efficiency (emptying).

Work & Wages

Wages are always distributed in the ratio of the total work done by each person. If they work for the same number of days, the wages are shared directly in the ratio of their efficiencies.

Alternate Days Work

Find the total work done in a complete cycle (e.g., 2 days for 2 people). Multiply the cycle to get as close to the total work as possible, then calculate the time for the remaining work done by the person whose turn is next.

Shortcut Trick

L.C.M. of fractions = L.C.M. of Numerators ÷ H.C.F. of Denominators

Numerators are 4, 5, and 8 ⇒ L.C.M.(4, 5, 8) = 40

Denominators are 7, 21, and 63 ⇒ H.C.F.(7, 21, 63) = 7

Required L.C.M. = 40/7

∴ The correct answer is 40/7.

Alternate Method

Given:

The fractions are 4/7, 5/21, and 8/63.

Formula Used:

L.C.M. of fractions = L.C.M. of Numerators ÷ H.C.F. of Denominators

Calculations:

⇒ First, we find the L.C.M. of the numerators (4, 5, and 8).

⇒ Prime factorization of 4 = 2²

⇒ Prime factorization of 5 = 5¹

⇒ Prime factorization of 8 = 2³

⇒ L.C.M.(4, 5, 8) = 2³ × 5 = 8 × 5 = 40

⇒ Next, we find the H.C.F. of the denominators (7, 21, and 63).

⇒ Prime factorization of 7 = 7¹

⇒ Prime factorization of 21 = 3¹ × 7¹

⇒ Prime factorization of 63 = 3² × 7¹

⇒ H.C.F.(7, 21, 63) = 7

⇒ Now, applying the formula: L.C.M. of fractions = 40 ÷ 7 = 40/7

∴ The correct answer is 40/7.

Additional Information

H.C.F. of Fractions

To find the Highest Common Factor of fractions, use the formula: H.C.F. of fractions = H.C.F. of Numerators ÷ L.C.M. of Denominators.

Product of Two Numbers

For any two numbers a and b, the product of their L.C.M. and H.C.F. is equal to the product of the numbers themselves: L.C.M.(a, b) × H.C.F.(a, b) = a × b.

Co-prime Numbers

If two numbers do not have any common prime factors, they are called co-prime numbers. Their H.C.F. is always 1, and their L.C.M. is simply their product.

Shortcut Trick

The average is computed directly by dividing the sum of all the observations by the total count.

Average = Total Sum ÷ Total Count

Average = 612 ÷ 10 = 61.2

∴ The correct answer is 61.2.

Alternate Method

Total Sum = 612 A A A . . . . A Total Numbers (N) = 10 Average (A) = 612 ÷ 10 = 61.2

Given:

⇒ Sum of 10 numbers = 612

⇒ Total numbers (N) = 10

Formula Used:

⇒ Average = Total Sum of Observations ÷ Total Number of Observations

Calculation:

⇒ Average = 612 ÷ 10

⇒ Average = 61.2

∴ The correct answer is 61.2.

Additional Information

Weighted Average

If a group has n₁ items with average A₁ and another group has n₂ items with average A₂, then the combined average = (n₁ × A₁ + n₂ × A₂) ÷ (n₁ + n₂).

Average of Consecutive Numbers

For a series of consecutive numbers or any arithmetic progression, the Average = (First Term + Last Term) ÷ 2.

Effect of Arithmetic Operations

If every observation in a dataset is increased, decreased, multiplied, or divided by a constant value 'k', the new average for that dataset will also increase, decrease, multiply, or divide by 'k' respectively.

Given:

3 / 2 + 15 x 3 - 5 = ? + 10

By using the BODMAS rule:

By, decoding the given symbols (interchanging '+' with '-' and 'x' with '/') we get.

Substituting the signs in the given equation (Let the question mark be 'x'):

⇒ 3 × 2 - 15 ÷ 3 + 5 = x - 10

⇒ 3 × 2 - (15 ÷ 3) + 5 = x - 10

⇒ (3 × 2) - 5 + 5 = x - 10

⇒ (6 + 5) - 5 = x - 10

⇒ 11 - 5 = x - 10

⇒ 6 = x - 10

⇒ x = 6 + 10

⇒ 16

Hence, the correct answer is 'Option 1'.

Shortcut Trick

Using the direct rule of alligation method for mixing two varieties:

Quantity Ratio = (Cost of Variety 2 − Mean Price) : (Mean Price − Cost of Variety 1)

Quantity Ratio = (150 − 145.50) : (145.50 − 130)

Quantity Ratio = 4.50 : 15.50

Quantity Ratio = 45 : 155 = 9 : 31

∴ The correct answer is 9 : 31.

Alternate Method

Given:

Cost of variety 1 (C₁) = ₹130 per kg

Cost of variety 2 (C₂) = ₹150 per kg

Mean price of the mixture (M) = ₹145.50 per kg

      130 150 145.50 4.50 15.50 Variety 1 Variety 2 Mean Price Ratio = 4.50 : 15.50

Formula Used:

Let the quantities of variety 1 and variety 2 be x and y respectively.

Weighted Average Price = (C₁ × x + C₂ × y) ÷ (x + y)

Calculations:

⇒ (130 × x + 150 × y) ÷ (x + y) = 145.50

⇒ 130x + 150y = 145.50(x + y)

⇒ 130x + 150y = 145.50x + 145.50y

⇒ 150y − 145.50y = 145.50x − 130x

⇒ 4.50y = 15.50x

⇒ x ÷ y = 4.50 ÷ 15.50

⇒ x ÷ y = 450 ÷ 1550

⇒ x ÷ y = 45 ÷ 155 = 9 ÷ 31

⇒ x : y = 9 : 31

∴ The correct answer is 9 : 31.

Additional Information

Rule of Alligation

When two ingredients of different prices are mixed, the ratio of their quantities is inversely proportional to the differences in their prices from the mean price. Ratio = (C₂ − M) : (M − C₁).

Weighted Average

It is used to find the average of two or more groups when their quantities and individual averages are known. Formula: A_w = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Replacement Method in Mixtures

If a container initially holds x units of pure liquid, and y units are drawn out and replaced with water n times, the final quantity of pure liquid remaining is: Final = x × (1 − y ÷ x)ⁿ.

The least possible Venn diagram for the given statement is:

Conclusions:

I. At least some magnets are lights - True (Because, some bulbs are lights and all bulbs are magnets, so the part of bulbs which is lights will also be magnets).

II. Some magnets are bulbs - True (Because, all bulbs are magnets, so some magnets will definitely be bulbs).

So, Both conclusions (I) and (II) follow.

Hence, the correct answer is "Option 4".

The correct answer is June to September.

Key Points

• Southwest monsoon is a significant climatic phenomenon in India, marking the rainy season for most parts of the country. It occurs between June and September.
• This period accounts for approximately 75-90% of India's annual rainfall, making it crucial for agriculture and water resources.
• The monsoon is driven by the seasonal reversal of wind systems and the difference in temperature between land and sea, causing moist winds from the Indian Ocean to sweep across the subcontinent.
• Regions such as the Western Ghats, northeastern states, and the Indo-Gangetic plains receive heavy rainfall during this period, benefiting agriculture and replenishing water bodies.
• The Indian Meteorological Department (IMD) monitors the onset, progression, and retreat of the monsoon season to aid in disaster preparedness and agricultural planning.

Additional Information

• Southwest Monsoon Mechanism:
• The monsoon originates due to the differential heating of land and sea. The intense heat over the Indian subcontinent creates low-pressure areas, attracting moist winds from the Indian Ocean.
• The winds are deflected due to the Coriolis effect, resulting in their southwest direction.
• Regional Impacts of the Monsoon:
• Regions such as Kerala experience the onset of the monsoon in early June, followed by other parts of the country.
• Northeastern states, including Meghalaya, receive some of the highest rainfall globally during this period.
• Agricultural Importance:
• India's agriculture is predominantly monsoon-dependent, with crops like rice, sugarcane, and cotton relying heavily on monsoon rains.
• A delayed or weak monsoon can lead to drought conditions, affecting crop yields and the economy.
• Retreat of the Monsoon:
• The withdrawal of the monsoon begins in September, starting from the northwest region and gradually retreating southward.
• Post-monsoon showers, also known as retreating monsoon, are common in Tamil Nadu and Andhra Pradesh.

Important Points

• Monsoon Forecasting:
• The Indian Meteorological Department (IMD) provides monsoon forecasts based on various models, including dynamical and statistical ones.
• Accurate forecasting helps in planning agricultural activities, managing water resources, and preparing for potential disasters like floods.
• Climate Change Impacts:
• Studies indicate that climate change is affecting the monsoon patterns, leading to uneven distribution of rainfall.
• Extreme events such as floods and droughts are becoming more frequent due to changing monsoon dynamics.
• Global Connections:
• The Indian monsoon is part of a larger atmospheric circulation system and is influenced by phenomena like El Niño and La Niña.
• El Niño events generally weaken the monsoon, while La Niña enhances it.

The correct answer is Karnataka.

Key Points

• Karnataka emerged as the winner of the Vijay Hazare Trophy 2024-25, showcasing an exceptional performance throughout the tournament.
• The Vijay Hazare Trophy is India’s premier domestic one-day cricket tournament, named after the legendary cricketer Vijay Hazare.
• Karnataka has a rich history in domestic cricket, and their consistent performances have made them one of the most successful teams in the tournament’s history.
• The team demonstrated a blend of strong batting, disciplined bowling, and excellent fielding to secure the championship.
• The tournament featured top domestic teams from across India, and Karnataka stood out due to their strategic gameplay and teamwork.

Additional Information

• About the Vijay Hazare Trophy:
• The tournament was started in 2002–03 and is organized by the Board of Control for Cricket in India (BCCI).
• It is a 50-over format tournament that serves as a platform for domestic players to showcase their talent and potentially get selected for the Indian national team.
• Teams represent different Indian states, cricket associations, and zones.
• Karnataka’s Dominance in Domestic Cricket:
• Karnataka has consistently been a strong contender in Indian domestic cricket, having won multiple Vijay Hazare Trophies in the past.
• The team boasts notable players, some of whom have represented India at the international level, including KL Rahul, Manish Pandey, and Mayank Agarwal.
• Significance of the Vijay Hazare Trophy:
• The tournament plays a crucial role in identifying and nurturing talent for the Indian cricket team, especially for the limited-overs format.
• It provides players with the opportunity to gain experience in high-pressure situations, similar to international cricket.
• Other Notable Teams in the 2024-25 Edition:
• Haryana: Known for producing legendary players like Kapil Dev, Haryana has a strong cricketing culture but fell short in this edition.
• Gujarat: A balanced team with a history of strong performances in the domestic circuit.
• Vidarbha: Emerging as a strong contender in recent years, especially in red-ball cricket, but couldn’t replicate the same success in the 2024-25 Vijay Hazare Trophy.

Important Points

• Historical Success: Karnataka’s victory in 2024-25 adds to their impressive track record, making them one of the most successful teams in the history of the Vijay Hazare Trophy.
• Emerging Talents: The tournament highlighted several young talents, some of whom are expected to represent India in the near future.
• Preparation for International Cricket: The Vijay Hazare Trophy acts as a breeding ground for players aiming to excel in international one-day cricket.
• Impact on Domestic Cricket: The competition enhances the overall quality of Indian domestic cricket by fostering healthy competition among teams.

The logic followed here is:

The given number series is: 57, 58, 62, 71, 87, 112, ?

Thus, the missing term in the series is 148.

Hence, the correct answer is "Option 3";

Given:

1. Only two people sit between K and T when counted from the right of K.
2. T sits to the immediate right of L.
3. Only three people sit between S and L when counted from the right of L.
4. J sits to the immediate right of R. 

 

Thus, J sits to the 4^th to the right of I.

Hence, the correct answer is "Option 1".