Search Previous Year Questions

Shortcut Trick

(35% - 30%) = 2000

5% = 2000 

⇒ 1% = 400

⇒ 70% = 28000

Cost Price of 1 sofa = Rs.28000

Alternate MethodCalculation:

Let pay amount of the sofa =  x 

According to question

Firstly after got discount of 30% = x - 30x% = 70x%

If got discount of 35% = x - 35x% = 65x%

So, 70x% - 65x% = 2000

⇒  5x% = 2000

⇒  x% = 400  

⇒ 70x% = 28000

∴ The correct answer is pay amount of sofa Rs. 28000.

Shortcut Trick

Product of co-prime ratios (x × y) = Product of numbers ÷ (HCF)²

x × y = 2352 ÷ (28 × 28) = 2352 ÷ 784 = 3

The factors of 3 are (1, 3). Since 3 is prime, the only co-prime pair is 1 and 3.

Greater number = HCF × Greater ratio = 28 × 3 = 84

∴ The correct answer is 84.

Alternate Method

Given: Product of two numbers = 2352, HCF = 28.

Formula Used: Product of two numbers = HCF × LCM; Number₁ = HCF × x, Number₂ = HCF × y (where x, y are co-prime).

⇒ Let the two numbers be 28x and 28y, where HCF(x, y) = 1.

⇒ (28x) × (28y) = 2352

⇒ 784 × xy = 2352

⇒ xy = 2352 ÷ 784

⇒ xy = 3

⇒ The only pair of co-prime numbers whose product is 3 is (1, 3).

⇒ Number₁ = 28 × 1 = 28

⇒ Number₂ = 28 × 3 = 84

⇒ Comparing 28 and 84, the greater number is 84.

∴ The correct answer is 84.

Additional Information

Fundamental Relation

For any two numbers a and b, HCF(a, b) × LCM(a, b) = a × b. This property is only valid for two numbers.

Co-prime Numbers

Two numbers are said to be co-prime if their Highest Common Factor (HCF) is 1. In the ratio method, the components remaining after dividing by HCF must be co-prime.

LCM and HCF Relationship

The LCM of a set of numbers is always exactly divisible by their HCF. LCM = HCF × (Product of remaining co-prime factors).

Given:

India needed 320 runs in 46 overs to win. 

In the first 10 overs, the average scoring rate was 5,

In the next 10 overs, it increased to 9. 

In the next 10 overs, it decreased to 5

Again increased to 8 in the next 10 overs. 

Formula Used:

Average Score = Total Run / Number of overs

Calculation:

By using the above formula,

Average Score = Total Run / Number of overs

Therefore,

Total run scored in 40 overs 

⇒ (10 × 5) + (10 × 9) + (10 × 5) + (10 × 8)

⇒   50 + 90 + 50 + 80 = 270

Remaining run = 320 - 270 = 50

Remaining over = 46 - 40 = 6

Average required = 50/6 = 8.3

∴ The correct answer is 8.3

Given:

Principle(P) = Rs 18000, Rate(R) = 6%, Time(T) = 2 years

Compounded Half-yearly

Formula used:

Amount = P(1 + R/100)^T

Amount = Principle + CI

Interest =  P{(1 + R/100)T - 1}

Calculation:

When it will be Compounded Half-yearly (6/12 ) then

Rate × 1/2 and Time × 2/1

R = 3% and T = 4 years

CI = 18000{(1 + 3/100)⁴ - 1}

⇒ 18000{(103/100)⁴ - 1}

⇒ 18000 × 0.1255088 = 2259 .15 ≈ Rs 2259.16

∴ The correct answer is Rs 2259.16

Given:

Mean(Average) of 30 observations = 35

31 written instead of 32

Formula used:

Mean = Sum of observation/number of observation

Calculation:

Let sum of 29 numbers is a and 30^th number be 31

(a + 31)/30 = 35

⇒ (a + 31) = 1050

But 31 was written instead of 32 so we have to add 1 on both sides

(a + 31 + 1) = 1051

So correct mean is 

1051/30 = 35.03

∴ The correct answer is 35.03

 Shortcut Trick31 written instead of 32 means original number is 1 more

+1/30 = +0.03

Mean should be +0.03 i.e 35 + 0.03 = 35.03

Shortcut Trick

Given the ratio x : y = 4 : 7, assume x = 4k and y = 7k.

Substitute these values into the second equation: 5(4k) + 4(7k) = 15

⇒ 20k + 28k = 15

⇒ 48k = 15 ⇒ k = 15/48 = 5/16

Now find x: x = 4 × (5/16) = 5/4 = 1.25

∴ The correct answer is 1.25.

Alternate Method

Given:

x/y = 4/7

5x + 4y = 15

x = 4k

y = 7k

5x + 4y = 15 5(4k) + 4(7k) = 15 20k + 28k = 15 48k = 15 k = 15/48 = 5/16

Calculations:

⇒ From the ratio x/y = 4/7, let x = 4k and y = 7k.

⇒ Substitute the values of x and y in the linear equation:

⇒ 5(4k) + 4(7k) = 15

⇒ 20k + 28k = 15

⇒ 48k = 15

⇒ k = 15 ÷ 48

⇒ k = 5/16

⇒ Substitute the value of k back to find x:

⇒ x = 4k = 4 × (5/16)

⇒ x = 5/4

⇒ x = 1.25

∴ The correct answer is 1.25.

Additional Information

Ratio & Proportion Rule

If two quantities are in the ratio a:b, they can be represented as ax and bx where x is a common constant multiplier. This allows reducing two variables into a single variable.

Substitution Method

In solving linear equations, isolating one variable in terms of the other and substituting it into the second equation easily determines the unknown single variable.

Shortcut TrickLet, Real CP of an article = Rs. X

Article sold at 20% loss.

If we take CP = Rs. 100, SP = (100 - 20) = Rs. 80

Now, X = (100 × 180/80) = Rs. 225

∴ The real CP is Rs. 225.

Alternate Method Given:

SP = Rs. 180

Sells at 20% loss

Concept:

SP = CP - CP × loss %

Calculation:

Let, CP of an article = Rs. X

SP = (X - X × 20/100) = 4X/5

Now,

4X/5 = 180

⇒ 4X = 900

⇒ X = 225

∴ The cost price of the article is Rs. 225.

Given:

Equal number of coins of 25 paise, 50 paise, and one rupee

Total value = Rs. 112

Calculation:

Let, no. of coins of each type = a

According to the question,

⇒ 25a + 50a + 100a = 11200

⇒ 175a = 11200

⇒ a = 64

∴ There are 64 coins in each type.

Concepts used:

BODMAS Rule

Calculation:

14.05 × 6.5 ÷ 0.5 

⇒14.05 × 13 = 182.65

∴ The correct answer is 182.65.

Given:

Two painters Neeraj and Sanoj painted the bungalow in 4 days.

Neeraj alone can paint the bungalow in 10 days.

Shortcut Trick

Efficiency of Sanoj = 10 - 4 = 6

∴ Sanoj complete total work = 40/6 = 6.67 days

Alternate Method

Concept Used:

If A does a work in n days then 1-day work of A is 1/n.

Calculation:

1 day's work of Neeraj & Sanoj = 1/4

1 day's work of Neeraj = 1/10

Let the total days required to complete the work by Sanoj be X.

Now, 1/10 + 1/X = 1/4

⇒ (X + 10)/10X = 1/4

⇒ 4 × (X + 10) = 10X

⇒ 4X + 40 = 10X

⇒ 10X - 4X = 40

⇒ 6X = 40 

⇒ X = 40/6 = 6.67 days

∴ Sanoj complete total work in 6.67 days