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Given:

Successive discounts are 30% and 20%

He sold it at Rs. 112 after two discounts

Concept used:

If two successive discounts are x% and y%, then total discount percentage is given by [x + y – xy/100]%

Calculation:

Total discount percentage = 30 + 20 – (30 × 20)/100

⇒ Total discount = 50 – 6 = 44%

Marked price × 56/100 = 112

Marked price = 112 × (100/56) = 200

∴ Marked price is Rs. 200

 

Let the marked price be Rs. x

After 30% discount,

Selling price = x – 0.30x = 0.70x

After allowing another successive discount of 20%,

∴ Selling price = 0.70x – [(0.70x) × 0.20] = 0.70x - 0.14x = 0.56x

According to the question,

⇒ 0.56x = 112

x = 112/0.56 = Rs. 200

∴ Marked price is Rs. 200

Given:

Passing marks percentage = 30%

Marks obtained by the student = 225

Fails by marks = 15

Concept used:

Maximum marks percentage = 100%

Calculation:

Amit gets 225 marks and fails by 15 marks

⇒ Pass marks = 225 + 15

⇒ 240 Marks

Now, according to question, percentage marks need to pass = 30%

⇒ 30% = 240 Marks

⇒ 100% = (240/30) × 100 Marks

⇒ 800 Marks

∴ Required Maximum marks = 800

Shortcut Trick Deviation of removed boxes from original average = 70 − 63 = 7 kg. Total weight deficit from 4 removed boxes = 4 × 7 = 28 kg. This deficit is distributed among the remaining 8 boxes. Reduction in average = 28 ÷ 8 = 3.5 kg. New Average = 63 − 3.5 = 59.5 kg. ∴ The correct answer is 59.5 kg.

Alternate Method Given: Total boxes = 12, Initial average = 63 kg, Removed boxes = 4, Removed average = 70 kg. Formula: Average = Sum of values ÷ Number of values

Remaining (8 Boxes) Removed (4) New Avg: ? Avg: 70 kg

Total: 12 Boxes (Avg: 63 kg)

⇒ Total weight of 12 boxes = 12 × 63 = 756 kg ⇒ Total weight of 4 removed boxes = 4 × 70 = 280 kg ⇒ Total weight of remaining boxes = 756 − 280 = 476 kg ⇒ Number of remaining boxes = 12 − 4 = 8 boxes ⇒ New average weight = 476 ÷ 8 = 59.5 kg ∴ The correct answer is 59.5 kg.

Additional Information Weighted Average Formula Combined Average = (n1A1 ± n2A2) ÷ (n1 ± n2), where n is the quantity and A is the average. Net Deviation Rule The sum of deviations of all observations from their arithmetic mean is always zero. This is used to find missing values or new averages quickly. Inclusion vs Exclusion When a person with weight 'W' is removed and average decreases, then W > Old Average. If average increases, then W < Old Average.

Shortcut Trick

Net Correction = Correct value − Wrong value = 43 − 23 = +20.

Increase in Average = Total Correction ÷ Number of subjects = 20 ÷ 5 = 4.

Correct Average = Old Average + Increase = 150 + 4 = 154.

∴ The correct answer is 154.

Alternate Method

Given:

Number of subjects (n) = 5

Incorrect average = 150

Correct value = 43

Wrong value = 23

Formula Used:

Correct Average = (Incorrect Total − Wrong value + Correct value) ÷ n

Calculations:

⇒ Incorrect sum of marks = 150 × 5 = 750

⇒ Correct sum of marks = 750 − 23 + 43

⇒ Correct sum of marks = 750 + 20 = 770

⇒ Correct average = 770 ÷ 5

⇒ Correct average = 154

∴ The correct answer is 154.

Additional Information

Average Definition

The average (arithmetic mean) is the ratio of the sum of observations to the total number of observations. Formula: Average = Σx ÷ n.

Correction in Average

When one or more values are misread, the Correct Average = Old Average + [(Correct Value − Incorrect Value) ÷ n].

Weighted Average

Used when different groups have different sizes: A_w = (n₁a₁ + n₂a₂) ÷ (n₁ + n₂).

Shortcut Trick

The extra time taken to cross the tunnel compared to the pole is used to cover the tunnel length.

Time difference = 20 s − 5 s = 15 s

Tunnel Length = Speed × Time difference = 90 × 15 = 1350 m.

∴ The correct answer is 1350 m.

Alternate Method

Given:

Speed of the train = 90 m/s

Time taken to cross a pole (t₁) = 5 s

Time taken to cross the tunnel (t₂) = 20 s

Formula Used:

Distance = Speed × Time

When crossing a pole, Distance = Length of Train (L_T)

When crossing a tunnel, Distance = Length of Train (L_T) + Length of Tunnel (L_Tunnel)

Train

Pole

Tunnel

t1 = 5s

t2 - t1 = 15s Speed = 90 m/s

Calculations:

⇒ L_T = 90 × 5 = 450 m

⇒ L_T + L_Tunnel = 90 × 20

⇒ 450 + L_Tunnel = 1800

⇒ L_Tunnel = 1800 − 450

⇒ L_Tunnel = 1350 m

∴ The correct answer is 1350 m.

Additional Information

Train Crossing Stationary Objects

When a train crosses a pole or a standing person, it covers a distance equal to its own length. When it crosses a platform or tunnel, it covers Distance = Length of Train + Length of Object.

Unit Conversion

To convert speed from km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.

Relative Speed

If two trains of lengths L₁ and L₂ cross each other, the total distance covered is always L₁ + L₂. Relative speed is S₁ + S₂ in opposite directions and |S₁ − S₂| in the same direction.

Given 

Amit's Capital = Rs 12000

Sumit's capital = Rs 15000

Time = 2 years 

Formula Used 

Investment = capital × time 

Investment ratio is directly proportional to Profit ratio 

Calculation 

⇒ Investment by Amit for 24 months = 12000 × 24 = Rs 288000

⇒ Investment by Sumit for 19 months = 15000 × 19 = Rs 285000

⇒ Investment Ratio = 288000 : 285000 = 96 : 95 

⇒ Profit Ratio = 96 : 95 

∴ the ratio of Amit and Sumit at the end of 2 years is 96 : 95

Given:

ENT specialists were 42° as per the pie chart.

Calculation:

As the circle is 360° which is equal to 60.

So the value of 1° = 60/360 = 1/6

So 42° = 42 × 1/6 = 7

∴ Option 3 is the correct answer.

Given

The total number of calculators sold by M and N is 700 and 800 respectively.

The total number of calculators sold by P and Q is 200 and 100 respectively.

According to the question,

The ratio of M and N to P and Q = (800 + 700) : (200 + 100 )

= 1500: 300

= 5 : 1

Calculation:

Total production of trucks in H and I = 400 + 300

⇒ 700

Total production of bikes in J and K = 350 + 400

⇒ 750

Ratio = 700 : 750

⇒ 14 : 15

∴ The required answer is 14 : 15.

Drawing the diagram as per the given instructions:

1) Lakshya walks towards south from his house and move towards east after walking 2m.

2) After walking 4m, he moves towards north and walks 5m.

3) From there he again moves towards east and walks 6m.

4) Finally he moves towards north and walks 2m to reach his office. 

Hence, Lakshya's office is in the North - East direction with respect to his house.