Search Previous Year Questions

Given: 

The principal is 800 rupee

Rate is 20%

Concept: 

SI = (P × R × T)/100

CI = P[(1 + r/100)n - 1]

Here, n is the number of terms in the year.

Calculation: 

The simple interest for 2 years

⇒ (800 × 20 × 2)/100

⇒ 8 × 20 × 2

⇒ 320 rupee

Now, Compound interest for 2 years is 

⇒ 800[(1 + 20/100)2 - 1]

⇒ 800[(120/100)2 - 1]

⇒ 800[(12/10)2 - 1]

⇒ 800 × [(144 - 100)/100]

⇒ 352 rupee 

Now, The difference between CI and SI is

⇒ 352 - 320

⇒ 32

∴ The difference between CI and SI is 32. 

Shortcut Trick

The difference between CI and SI for 2 years is P(r/100)2

The  difference is 

⇒ 800(20/100)2

⇒ 800 × (1/5)2

⇒ 32

∴ The difference between CI and SI is 32. 

Important Points

This short trick works only for 2 years.

Shortcut TrickLet the income of Rajesh be 100.

 

⇒ Percentage increase in expenditure = [(120 - 95)/95] × 100

⇒ Percentage increase in expenditure = (25/95) × 100 ≈ 26%

∴ The correct answer is Option 4).

Given:

Rajesh saving = 5%

Income increased = 25%

Formula used

Income = expenditure + saving

Calculation

Let income be 100

Given saving = 5% of 100 = 5

Expenditure = 100 – 5 = 95

The income increased by 25%

New income = 25% of 100 + 100 = 125

Saving is the same = 5

Then expenditure = 120

Change in expenditure = 120 – 95 = 25

Therefore, Percentage increase = (25 ÷ 95) × 100 = 26.31% ≈ 26%

∴ Percentage increase in his expenditure is 26%

Given:

The profit ratio of Rajeev : Abhay = 2 : 3.

Rajeev's invested amount = Rs. 40,000.

Concept used:

Amount invested Rajeev to Abhay = Ratio of their Profit

Calculation:

The amount of Rajeev invested Rs. 40000 and amount invested by Abhay is y.

Amount invested Rajeev to Abhay = Ratio of their profit

⇒ 40000/y = 2/3

⇒ y = 40000 × 3/2

⇒ y = Rs. 60000

∴ The amount invested by Q is Rs. 60000.

Given:

The listed price of the cycle = Rs. 20,000

Selling price to the retailer = Rs. 14,000

Formula:

Percent discount = (Discount / Listed price) * 100

Calculation:

To calculate the percent discount, we need to find the discount first.

Discount = Listed price - Selling price

Substituting the given values:

Discount = Rs. 20,000 - Rs. 14,000

= Rs. 6,000

Now, we can calculate the percent discount:

Percent discount = (Discount / Listed price) * 100

= (6000 / 20000) * 100

= 30

Therefore, the percent discount given to the retailer is 30%.

Calculation:

In the school ratio of boys : girls = 12 : 13

Now, 12 unit → 372, 

Then, (12 + 13) = 25 unit  → 372/12 × 25 = 775

∴ The correct answer is 775

Shortcut Trick

Student's scored percentage = Passing percentage − Failing gap percentage

Scored percentage = 40% − 20% = 20%

Since 20% of the maximum marks corresponds to the 40 marks obtained:

Maximum marks = (40 ÷ 20) × 100 = 200

∴ The correct answer is 200 marks.

Alternate Method

Given:

Marks obtained by the student = 40 marks

Failing gap = 20% of maximum marks

Passing percentage = 40% of maximum marks

Formula Used:

Passing Marks = Obtained Marks + Shortfall Marks

0% 20% 40% (Pass) 100%

Scored Failed by

40 Marks

20% Gap

Max Marks = 100% = 200 Marks

Calculations:

Let the maximum marks be x.

⇒ Passing marks = 40% of x = 0.4x

⇒ Shortfall (Failed by) marks = 20% of x = 0.2x

⇒ Obtained marks + Shortfall marks = Passing marks

⇒ 40 + 0.2x = 0.4x

⇒ 0.4x − 0.2x = 40

⇒ 0.2x = 40

⇒ x = 40 ÷ 0.2

⇒ x = 200

∴ The correct answer is 200 marks.

Additional Information

Concept of Passing Marks

If a student scores 'M' marks and fails by 'X' marks, then Passing Marks = M + X. If they score 'N' marks and get 'Y' marks above passing, then Passing Marks = N − Y.

Fraction Equivalent Strategy

Converting percentages to fractions speeds up calculations. 20% = 1/5 and 40% = 2/5. Here, (2/5)x − (1/5)x = 40 ⇒ (1/5)x = 40 ⇒ x = 200.

Percentage Base Rule

Whenever a percentage is mentioned (like 20% failed marks), it is always calculated on the Total/Maximum Marks of the exam unless specified otherwise.

Given:

Speed of going = 40 km/h,

Speed of returning = 60 km/h

Concept:

Average speed = Total distance / Total time.

The total distance for the round trip is twice the one-way distance.

Solution:

One-way distance = d

⇒ Total time = d/40 + d/60 = (3d + 2d)/120 = d/24

⇒ Average speed = 2d/(d/24) = 48 km/h

Hence, her average speed is 48 km/h.

Shortcut Trick

Relative Speed = Distance ÷ Time = 150 ÷ 3 = 50 m/s.

Convert relative speed to km/h: 50 × (18 ÷ 5) = 180 km/h.

Since both are moving in the same direction, Relative Speed = Speed of Train − Speed of Man.

180 = Speed of Train − 2 ⇒ Speed of Train = 182 km/h.

∴ The correct answer is 182 km/h.

Alternate Method

Given:

Length of the train = 150 m

Time taken to pass the man = 3 s

Speed of the man = 2 km/h

Formula Used:

Distance = Relative Speed × Time

Speed in m/s = Speed in km/h × (5 ÷ 18)

Calculations:

Let the speed of the train be v km/h.

⇒ Relative speed of train with respect to the man = (v − 2) km/h

⇒ Convert km/h to m/s = (v − 2) × (5 ÷ 18) m/s

⇒ Distance covered = Length of the train = 150 m

⇒ Time taken = 3 s

⇒ 150 = [(v − 2) × (5 ÷ 18)] × 3

⇒ 150 = (v − 2) × (15 ÷ 18)

⇒ 150 = (v − 2) × (5 ÷ 6)

⇒ v − 2 = 150 × (6 ÷ 5)

⇒ v − 2 = 30 × 6

⇒ v − 2 = 180

⇒ v = 180 + 2

⇒ v = 182 km/h

∴ The correct answer is 182 km/h.

Additional Information

Relative Speed (Same Direction)

When two objects move in the same direction, their relative speed is the difference of their individual speeds: S_rel = S₁ − S₂.

Relative Speed (Opposite Direction)

When two objects move in opposite directions, their relative speed is the sum of their individual speeds: S_rel = S₁ + S₂.

Speed Conversion Rules

To convert km/h to m/s, multiply the speed value by (5 ÷ 18). Conversely, to convert m/s to km/h, multiply by (18 ÷ 5).

Given:

Santosh got 24000 more votes than Mantosh

Mantosh and Santosh got 30% and 40% of the total votes respectively

Shortcut Trick

10% = 24000

1% = 2400

100% = 240000

Therefore, total number of votes are 240000.

Alternate Method Concept:

Calculation of total votes based on percentage shares of candidates.

Solution:

Let the total number of votes be X

As per the question,

Santosh's votes (40% of X) = Mantosh's votes (30% of X) + 24000

⇒ 40/100 × X = 30/100 × X + 24000

⇒ 10/100 × X = 24000

⇒ X = 240000

Therefore, total number of votes are 240000.

We have checked the each option,

Option (1): 3, 2, 5, 6, 8, 1, 4, 7

The word formed from jumbled letters is "DAHESION" which is Not a Meaningful word.

Option (2): 2, 3, 5, 6, 4, 8, 1, 7

The word formed from jumbled letters is "ADHEOSIN" which is Not a Meaningful word.

Option (3): 2, 3, 5, 6, 8, 1, 4, 7

The word formed from jumbled letters is "ADHESION" which is  a Meaningful word.

Option (4): 2, 3, 5, 6, 8, 4, 1, 7

The word formed from jumbled letters is "ADHESOIN" which is Not a Meaningful word.

Hence, the correct answer is "2, 3, 5, 6, 8, 1, 4, 7".