Search Previous Year Questions

Given:

Principal (P) = 12,500

Amount (A): 15,500

Time (t) = 4 year

Formula used:

\(S.I. = \frac{P \times R \times t}{100}\)

S.I = Amount - Principal

Calculation:

⇒ S.I. = 15,500 - 12,500

⇒ S.I. = 3,000

⇒ \(3,000 = \frac{12,500 \times R \times 4}{100}\)

⇒ \(R = \frac{3000 \times 100}{12,500 \times 4}\)

⇒ R = 6%

∴ correct answer is 6%

Given:

Y has to score 40% marks to pass.

He gets 20 marks and fails by 40 marks

Calculation:

Let the maximum marks be x

According to the question,

⇒ 40 + 20 = 0.4 x 

⇒ 0.4 x = 60 = 150

∴  The maximum mark of the exam is 150,

Shortcut Trick

Sum of the first 5 natural numbers = 5 × 3 = 15

New sum after adding the number 2 = 15 + 2 = 17

New total number of observations = 5 + 1 = 6

New average = 17 ÷ 6 ≈ 2.83

∴ The correct answer is 2.83.

Alternate Method

Given:

Average of the first five natural numbers = 3

The new number to be added = 2

Formula Used:

Average = Sum of all observations ÷ Total number of observations

Calculations:

⇒ The first five natural numbers are 1, 2, 3, 4, and 5.

⇒ Initial Sum = 1 + 2 + 3 + 4 + 5 = 15

⇒ Total count of numbers initially = 5

⇒ New Sum after adding the number 2 = 15 + 2 = 17

⇒ New total count of numbers = 5 + 1 = 6

⇒ New Average = New Sum ÷ New Count

⇒ New Average = 17 ÷ 6 = 2.833...

⇒ New Average ≈ 2.83

∴ The correct answer is 2.83.

Additional Information

Average Formula

Average = Sum of all observations ÷ Total number of observations.

Sum of First 'n' Natural Numbers

The sum of the first 'n' natural numbers can be directly calculated using the formula: S = n × (n + 1) ÷ 2.

Combined Average

When combining multiple groups or adding new values, the new average is evaluated as (Total Old Sum + New Values Sum) ÷ (Total Old Count + New Count).

Shortcut Trick

Marked Price (MP) = Rs. 1600

Discount% = 10%

Multiplier for SP = (100 − 10) ÷ 100 = 0.9

Selling Price (SP) = 1600 × 0.9 = 1440

∴ The correct answer is Rs. 1440.

Alternate Method

Given: Marked Price = Rs. 1600, Discount Rate = 10%

Formulas: Discount = MP × (Discount% ÷ 100) | SP = MP − Discount

⇒ Discount = 1600 × (10 ÷ 100) = Rs. 160

⇒ Selling Price (SP) = 1600 − 160

⇒ Selling Price (SP) = Rs. 1440

∴ The correct answer is Rs. 1440.

Additional Information

Marked Price (MP)

The price printed on an item or the label price is called the Marked Price. Discounts are always calculated on this value.

Selling Price (SP)

The actual price at which the item is sold to the customer after deducting the discount from the MP.

Given:

Ratio of ages = 2 : 3 : 4 : 5

Total age = 140 years

Formula Used:

Age of individual = (Ratio part of individual / Sum of ratio parts) × Total age

Calculations:

Sum of ratio parts = 2 + 3 + 4 + 5

⇒ Sum of ratio parts = 14

Age of youngest person (2 parts) = \(\dfrac{2}{14}\) × 140

⇒ Age of youngest person = 2 × 10

⇒ Age of youngest person = 20 years

Age of oldest person (5 parts) = \(\dfrac{5}{14}\) × 140

⇒ Age of oldest person = 5 × 10

⇒ Age of oldest person = 50 years

Difference in age = Age of oldest person - Age of youngest person

⇒ Difference in age = 50 - 20

⇒ Difference in age = 30 years

∴ The difference in age between the youngest and the oldest person is 30 years.

Shortcut Trick

Multiply the expenditure ratio by 2 to equalise the differences between the ratios.

Income ratio = 9 : 7

Expenditure ratio = (4 : 3) × 2 = 8 : 6

Savings in parts = Income − Expenditure = (9 − 8) = 1 part for A and (7 − 6) = 1 part for B.

Given 1 part = Rs. 200.

Sum of their incomes = (9 + 7) parts = 16 × 200 = Rs. 3200.

∴ The correct answer is Rs. 3200.

Alternate Method

Given:

Ratio of incomes of A and B = 9 : 7

Ratio of expenditures of A and B = 4 : 3

Savings of each per week = Rs. 200

Income = Expenditure + Savings

A:

Income: 9x

Exp: 9x − 200 200

B:

Income: 7x

Exp: 7x − 200 200

Exp Ratio → (9x − 200) : (7x − 200) = 4 : 3

Formula Used:

Income = Expenditure + Savings

Calculations:

⇒ Let the incomes of A and B be 9x and 7x respectively.

⇒ Expenditure of A = (9x − 200)

⇒ Expenditure of B = (7x − 200)

⇒ According to the given data, (9x − 200) / (7x − 200) = 4 / 3

⇒ 3 × (9x − 200) = 4 × (7x − 200)

⇒ 27x − 600 = 28x − 800

⇒ 28x − 27x = 800 − 600

⇒ x = 200

⇒ Sum of their weekly incomes = 9x + 7x = 16x

⇒ 16 × 200 = Rs. 3200

∴ The correct answer is Rs. 3200.

Additional Information

Ratio Balancing Method

When a constant value is added or subtracted from two terms of a ratio, the difference between the terms must remain constant. Equalise the difference between parts to solve directly without equations.

Cross-Multiplication Trick

For initial ratio a : b, changed to c : d by adding/subtracting x and y: the value of 1 part = (c × y − d × x) ÷ (a × d − b × c).

Income, Expenditure & Savings

The fundamental relation is always Income = Expenditure + Savings. This applies equivalently to monthly, weekly or annual data as long as units remain consistent.

Given

Bag contains Rs. 1, 50 paise, coins

The ratio of value is 30 : 11

The total no. of coins are 520

Concept used

Ratio concept used

Calculation

Value of Rs. 1 and 50 paise coins = 30 : 11

Number of coins = 30 : 22

⇒ 52 part = 520

⇒ 1p = 10

⇒ 22p = 10 × 22

⇒ 220

Calculation:

Rs. 1 = 100 paise 

Let the total number of 100 paise coins be x

Then 50 paise coins are 520 – x

According to the question,

⇒ 100x/50(520 – x) = 30/11

⇒ 11 × 100x = 30 × 50(520 – x)

⇒ 1,100x = 7,80,000 – 1,500x

⇒ 2,600x = 7,80,000

⇒ x = 7,80,000/2,600

⇒ x = 300

50 paise coins,

⇒ 520 – 300 = 220

∴ 50 paise coins are 220.

Total expense = 360°

Expense on clothes = 50°

Let, expense on cloth = Rs. x

According to problem,

⇒ 50/360 = x/108000

⇒ x = 1080000 × 5/36

⇒ x = 150000

∴ They spent on cloths = Rs. 150000

Given:

Formula used:

Average = Sum of observation/Total number of observation

Calculation:

Total cars used by three types of people's = 1000 + 500 + 2000 = 3500

∴ Required average = 3500/3 = 1166.66 ≈ 1167

According to the English alphabets and their positional values: 

The pattern followed in the given series is:  

• First alphabet is decreased to 7 positional values.
• Second alphabet is decreased to 8 positional values.
• Third alphabet is decreased to 9 positional values.

Hence the correct answer is option 2).