ADRE Higher Secondary (HSSLC) Level Paper III 2024 Complete Question Paper Solution with Explanations of General Mathematics Section

ADRE Higher Secondary (HSSLC) Level Paper III 2024 Complete Solved Paper with Detailed Explanations of General Mathematics Section

The General Mathematics section is a vital part of competitive examinations, designed to assess a candidate’s numerical ability, mathematical concepts, and problem-solving skills. This section tests how quickly and accurately candidates can perform calculations, interpret numerical data, and apply mathematical formulas to solve practical problems. Strong mathematical aptitude not only helps in scoring higher but also improves overall exam performance through better speed and accuracy.

The General Mathematics section typically includes topics such as arithmetic, percentage, profit and loss, ratio and proportion, averages, simple and compound interest, time and work, time, speed and distance, algebra, geometry, mensuration, number system, simplification, data interpretation, and basic statistics. Consistent practice, conceptual clarity, and effective time management are the keys to achieving a high score in this section.

General Mathematics Section

• Total Questions : 35
• Total Marks : 35
• Nagative Marking : 0.25%

Q1. A number was increased by 40% and thereafter decreased by 40%. The net change in the number in percentage is

(A) 16% increase

(B) 16% decrease

(C) 32% decrease

(D) No change

Answer: (B) 16% decrease

Explanation

Method 1

• Assume the original number is 100.
• Increase by 40%
• So, 100 → 140

Now decrease 140 by 40%:

• 40% of 140 = 56
• 140 − 56 = 84

Compare with the original number:

• Original = 100
• Final = 84
• Loss = 16

So, the net change is 16% decrease.

Method 2

Quick Exam Trick

Whenever a number is increased by x% and then decreased by the same x%,

Net Change = −x²/100 percentage

Here,  x = 40

Therefore,  -(40) 2 / 100 = -1600 / 100 = -16 

So, the result is 16% decrease.

• [Minus means Decrease & Plus means Increase]
• Method 2 is easy, shortcut and simple

Q2. If the average age of A, B and C is 22 years and the average age of B and C is 25 years, then find the age of A after 9 years from now.

(A) 25 years

(B) 35 years

(C) 50 years

(D) 45 years

Answer: (A) 25 years

Explanation

Method 1

Step 1: Find the total age of A, B and C.

• Average = 22
• Number of persons = 3

So, Total age = 22 × 3 = 66 years

Step 2: Find the total age of B and C.

• Average = 25
• Number of persons = 2

So, Total age = 25 × 2 = 50 years

Step 3: Find A's present age.

• A's present age = 66 − 50 = 16 years

Step 4: Find A's age after 9 years.

• 16 + 9 = 25 years

Method 2

Shortcut Method

Given:

• Average of A, B & C = 22
• Average of B & C = 25

Shortcut Formula:

  A's present age  = (Average of 3 × 3) − (Average of 2 × 2)

                                              = 22 × 3 − 25 × 2

                                            = 66 − 50

                                         = 16 years

After 9 years: = 16 + 9 = 25 years

One-Line Trick : 

(22×3)−(25×2)+9=25

Q3. The smallest among √(1/2), √(1/3), √(1/4) and √(2/3) is:

(A) √(1/2)

(B) √(1/3)

(C) √(1/4)

(D) √(2/3)

Correct Answer: (C) √(1/4)

Explanation

The square root (√) is an increasing function. This means:

If a < b, then √a < √b.

So, first compare the numbers inside the square roots:

• 1/2 = 0.50
• 1/3 ≈ 0.33
• 1/4 = 0.25 ( Smallest ) [ After Point it is 2 but others are more than 2 ]
• 2/3 ≈ 0.67

Since

1/4​ < 1/3​ < 1/2​ < 2/3​,

taking square roots gives:

√(1/4) < √(1/3)  < √(1/2) < √(2/3)

Therefore, the smallest is: (C) √(1/4)

[Note: 0.1 < 0.2 < 0.3 < 0.4 < 0.5 ans so on ]

Shortcut Trick

When all numbers are under the square root (√), compare the numbers inside the root.

The smallest number inside is 1/4, so the smallest value is √(1/4).

Q4. If x : y : z = 3 : 4 : 7, then (x+y+z) / z is equal to:

(A) 2

(B) 3

(C) 4

(D) 5

Answer: 2

Solution

Given:   x:y:z=3:4:7

Let, x=3k, y=4k, z=7k

Then,   (x+y+z) / z = (3k + 4k + 7k ) / 7k = 14k / 7k = 2

Shortcut Trick

When given a ratio, substitute the ratio values directly:

( 3+ 4 + 7 ) / 7 = 14 / 7 = 2

Q5. Two numbers are in the ratio 2 : 3 and the product of their HCF and LCM is 96. The sum of the two numbers is

(A) 18

(B) 20

(C) 22

(D) 24

Correct Answer: (B) 20

Solution

Let the numbers be:

2X and 3X

Since 2 and 3 are co-prime,

So, 

• HCF = X
• LCM = 6X

Given:

HCF × LCM = 96

=> X × 6X=96

=> 6X2=96

=> X2=16

=> X = 4

Therefore, the numbers are:

• 2X = 2 x 4 = 8
• 3X = 3x 4 = 12

Therefore, Sum = 8 + 12 = 20

[ Remember : HCF × LCM = Product of the two numbers ]

Q6. The value of ∛(8²) is:

(A) 1

(B) 3

(C) 2

(D) 4

Correct Answer: (D) 4

Solution

∛(8²) = ∛64 =  ∛(4³) = (4³)^(1/3) = 4^(3×1/3) = 4¹ = 4

Rule to remember:

ⁿ√(aᵐ) = (aᵐ)^(1/n) = a^(m/n)

Q7. A certain amount invested in a firm would become double at the end of one month, but it deducts an amount of ₹ 120 on every doubling. A person invests an amount of ₹ 105 and continues for 3 months without investing any additional amount. At the end of 3 months, his net income is

(A) ₹ 55

(B) ₹ 0

(C) ₹ 270

(D) ₹ 45

Correct Answer: (B) ₹ 0

Solution

Shortcut Trick

Given amount ₹ 105.

• Month 1: 105×2−120=90
• Month 2: 90×2−120=60
• Month 3: 60×2−120=0

[ 2 is multiplied due to double and do minus 120 as question says 120 deduction ]

Q8. The count of prime numbers between 80 and 100 is

(A) 2

(B) 5

(C) 3

(D) 4

Correct Answer: (C) 3

Solution

Prime numbers between 80 and 100 are:

• 83 , 89 & 97

Important Web Links For You 

FAQs

Q1. Which subjects are covered in Questions 1–30 of the ADRE HSSLC Level 2024 Social Studies section?

Ans: Questions 1–30 mainly cover Geography, Indian Geography, General Science, Indian Awards, and important world facts, helping candidates test their basic social studies knowledge. 

GeographicReference

Q2. Are the answers to ADRE HSSLC 2024 Social Studies Questions  1–30   officially verified?

Ans: Yes. The correct answers are verified using the official ADRE HSSLC Level 2024 final answer key, while the explanations are written independently to help candidates understand the concepts.

Q3. Are detailed explanations provided for every question?

Ans: Yes. Every question includes a detailed explanation to help candidates understand why the correct option is right and improve their preparation for future ADRE examinations.

Q4. Is this solved paper useful for upcoming ADRE examinations?

Ans: Yes. Previous year question papers help candidates understand the exam pattern, important topics, and frequently asked questions, making them an essential resource for ADRE preparation.

Q5. Where can I find solutions for the remaining ADRE HSSLC Level 2024 questions?

Ans: You can explore the complete subject-wise solutions on RozgarAssam, including Social Studies, General Knowledge, Logical Reasoning & Mental Ability, General English, and General Mathematics, along with detailed explanations for all 150 questions.