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Ratio of Boys to Girls = 100 : 60 = 5 : 3.

Using weighted average deviation: Total deviation = 80 × (30 − 24) = 480 (sum deficiency from girls).

Weight deviation of boys = (30 − 24) × 3 / 5 = 3.6 kg above average.

Average weight of boys = 30 + 3.6 = 33.6 kg.

Difference = 33.6 − 24 = 9.6 kg.

∴ The correct answer is 9.6 kg.

Alternate Method

Given: Total students = 80, Average = 30 kg, Girls = 40% less than Boys.

Formula Used: Average = Total Sum ÷ Number of observations

⇒ Let Boys = B and Girls = G. G = B − 0.40B = 0.60B.

⇒ B + 0.60B = 80 ⇒ 1.6B = 80 ⇒ B = 50, G = 30.

⇒ Total Weight = 80 × 30 = 2400 kg.

⇒ Total weight of Girls = 30 × 24 = 720 kg.

⇒ Total weight of Boys = 2400 − 720 = 1680 kg.

⇒ Average weight of Boys = 1680 ÷ 50 = 33.6 kg.

⇒ Difference = 33.6 − 24 = 9.6 kg.

∴ The correct answer is 9.6 kg.

Additional Information

Weighted Average Formula

Used when two or more groups are combined: Average = (n₁w₁ + n₂w₂) ÷ (n₁ + n₂).

Alligation Method

The ratio of the number of items is equal to the inverse ratio of the deviations from the mean: (Value₁ − Mean) ÷ (Mean − Value₂) = n₂ ÷ n₁.

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Total age of Sahil, Tanya, and Deepak = 72 years.

Total age of Sahil and Tanya = 22 × 2 = 44 years.

Age of Deepak = 72 − 44 = 28 years.

Ratio of Sahil to Deepak = 5 : 7 → (7 units = 28 years ⇒ 1 unit = 4 years).

Age of Sahil = 5 × 4 = 20 years.

Age of Tanya = 44 − 20 = 24 years.

∴ The correct answer is 24 years.

Alternate Method

Given: Average age (Sahil + Tanya) = 22, Ratio (Sahil : Deepak) = 5 : 7, Total age = 72.

Formula Used: Total Sum = Average × Number of entities.

⇒ Sum of Sahil (S) and Tanya (T) = 22 × 2 = 44 years.

⇒ Age of Deepak (D) = (S + T + D) − (S + T) = 72 − 44 = 28 years.

⇒ Let Sahil's age be 5x and Deepak's age be 7x.

⇒ 7x = 28 ⇒ x = 4.

⇒ Sahil's age = 5 × 4 = 20 years.

⇒ Tanya's age = (S + T) − S = 44 − 20 = 24 years.

∴ The correct answer is 24 years.

Additional Information

Average Age Concept

Average = Sum of observations ÷ Total number of observations. To find the sum, multiply the average by the count.

Ratio and Proportion

If the ratio is a:b, then actual values can be assumed as ax and bx. The value of x is found by equating a known part to its ratio unit.

Ages in the Future/Past

To find age 'n' years hence, add n to the present age. To find age 'n' years ago, subtract n from the present age.

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Simple Interest is 1/5 of Principal (P), which is 20%.

Rate is 10% per annum, so Time (T) = 20% ÷ 10% = 2 years.

New time = T + 3 = 2 + 3 = 5 years.

Interest in 5 years at 10% = 50% of P = 0.5 P.

Amount = P + 0.5 P = 1.5 P.

∴ The correct answer is 1.5 P.

Alternate Method

Given: Interest (I) = P/5, Rate (R) = 10%.

Formula Used: SI = (P × R × T) / 100; Amount = P + SI.

⇒ P/5 = (P × 10 × T) / 100

⇒ 1/5 = T / 10

⇒ T = 10 / 5 = 2 years

⇒ New Time = T + 3 = 2 + 3 = 5 years

⇒ New Simple Interest = (P × 10 × 5) / 100 = 50P / 100 = 0.5 P

⇒ Final Amount = P + 0.5 P = 1.5 P

∴ The correct answer is 1.5 P.

Additional Information

Simple Interest Formula

The basic formula is SI = (P × R × T) / 100, where P is Principal, R is Rate, and T is Time.

Amount Calculation

Total Amount (A) is the sum of Principal (P) and Simple Interest (SI): A = P + SI = P(1 + RT/100).

Rate and Fraction Relation

If interest is 1/n of principal in T years, then R × T = 100/n percent.

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Total Income = ₹36,000

Expenditure (Food + Education) = 25% + 12% = 37% of ₹36,000 = ₹13,320

Left Amount = ₹2,160

Bank Savings = Total Income − (Expenditure + Left Amount) = 36,000 − (13,320 + 2,160)

Bank Savings = 36,000 − 15,480 = ₹20,520

∴ The correct answer is ₹20,520.

Alternate Method

Given: Monthly Income = ₹36,000 | Food = 25% | Education = 12% | Left = ₹2,160

⇒ Expense on Food = 25% of 36,000 = 36,000 × (25/100) = ₹9,000

⇒ Expense on Education = 12% of 36,000 = 36,000 × (12/100) = ₹4,320

⇒ Left Amount = ₹2,160

⇒ Total accounted for (except bank savings) = 9,000 + 4,320 + 2,160 = ₹15,480

⇒ Bank Savings = 36,000 − 15,480 = ₹20,520

∴ The correct answer is ₹20,520.

Additional Information

Percentage Change

To find the percentage of a value, use (Value/Total) × 100. For successive changes, use a + b + (ab/100).

Income and Expenditure

Total Income = Total Expenditure + Total Savings. Savings can be further divided into bank deposits and cash-in-hand (left amount).

Base Change Rule

If expenses are given as a percentage of the remaining balance, the calculation must be done sequentially: Remaining = Original × (100−r₁)/100 × (100−r₂)/100.

Shortcut Trick

Speed of Train = Difference in length ÷ Difference in time

⇒ Speed = (180 − 140) ÷ (20 − 18) = 40 ÷ 2 = 20 m/s

Convert to kmph: 20 × (18 ÷ 5) = 4 × 18 = 72 kmph

∴ The correct answer is 72 kmph.

Alternate Method

Given: Length of train = x m, Lengths of platforms = 140 m and 180 m, Times taken = 18 sec and 20 sec.

Formula Used: Speed = Total Distance ÷ Total Time; Total Distance = Length of Train + Length of Platform.

⇒ Speed = (x + 140) ÷ 18 = (x + 180) ÷ 20

⇒ 20(x + 140) = 18(x + 180)

⇒ 10(x + 140) = 9(x + 180)

⇒ 10x + 1400 = 9x + 1620

⇒ x = 220 m

⇒ Speed = (220 + 140) ÷ 18 = 360 ÷ 18 = 20 m/s

⇒ Speed in kmph = 20 × (18/5) = 72 kmph

∴ The correct answer is 72 kmph.

Additional Information

Unit Conversion

To convert m/s to kmph, multiply by 18/5. To convert kmph to m/s, multiply by 5/18.

Relative Speed

When two objects move in opposite directions, relative speed = S₁ + S₂. In same direction, relative speed = |S₁ − S₂|.

Train Crossing Object

When a train crosses a pole or a man, distance = length of train. When it crosses a bridge or platform, distance = length of train + length of platform.

7 persons – B, C, D, E, F, G and H 

1. G sits three places away from D.

    From this we get the possible arrangements.

   

 

 

2. Only one person sits between B and G.
3. B sit neither adjacent to D nor at the end.

    

 

 

 

4. Number of persons to the left of H is the same as the number of persons to the right of C.
5. C sits to the right of G and to the immediate left of E.

     From this case 2 is eliminated, as we cannot place E. In case of 1, C and E sit to the immediate right and second to the right of G.

     Thus, F sits at the left end. The final arrangement is as follows.

Hence, F sits second to the left to H.

7 persons – B, C, D, E, F, G and H 

1. G sits three places away from D.

    From this, we get the possible arrangements.

    

 

 

 

 

2. Only one person sits between B and G.
3. B sits neither adjacent to D nor at the end.

 

 

 

 

 

4. Number of persons to the left of H is same as number of persons to the right of C.
5. C sits to the right of G and to the immediate left of E.

     From this case 2 is eliminated, as we cannot place E. In case of 1, C and E sit to the immediate right and second to the right of G.

     Thus, F sits at the left end. The final arrangement is as follows.

Except DG, first person sits to the left of the second person. 

Therefore, DG is the correct answer.

7 persons – B, C, D, E, F, G and H 

1. G sits three places away from D.

From this, we get the possible arrangements.

 

 

 

2. Only one person sits between B and G.
3. B sit neither adjacent to D nor at the end.

 

 

 

 

4. Number of persons to the left of H is same as number of persons to the right of C.
5. C sits to the right of G and to the immediate left of E.

     From this case 2 is eliminated, as we cannot place E. In case of 1, C and E sit to the immediate right and second to the right of G.

     Thus, F sits at the left end. The final arrangement is as follows.

Hence, 'G sits in the middle of the row' is true.

7 persons – B, C, D, E, F, G and H 

1. G sits three places away from D means there are two person between G and D.

    From this we get the possible arrangements.

 

 

 

2. Only one person sits between B and G.
3. B sit neither adjacent to D nor at the end.

 

 

 

 

4. Number of persons to the left of H is same as number of persons to the right of C.
5. C sits to the right of G and to the immediate left of E.

     From this case 2 is eliminated, as we cannot place E. In case of 1, C and E sit to the immediate right and second to the right of G.

     Thus, F sits at the left end. The final arrangement is as follows.

E sits adjacent to D. B is 4^th left from E. 

Hence, B sits four places away from the person who sits adjacent to D.

7 persons – B, C, D, E, F, G and H 

1. G sits three places away from D.

    From this we get the possible arrangements.

 

 

 

2. Only one person sits between B and G.
3. B sit neither adjacent to D nor at the end.

 

 

 

 

4. Number of persons to the left of H is same as number of persons to the right of C.
5. C sits to the right of G and to the immediate left of E.

     From this case 2 is eliminated, as we cannot place E. In case of 1, C and E sit to the immediate right and second to the right of G.

     Thus, F sits at the left end. The final arrangement is as follows.

Hence, two persons are sitting between H and E.