Question 1

The sum of two numbers is 48. If one number is twice the other, what is the smaller number?

Accepted Answer

Step 1: Let the smaller number be x. Then the larger number is 2x. Step 2: Form the equation: x + 2x = 48 → 3x = 48. Step 3: x = 48 / 3 = 16. Therefore, the smaller number is 16.

Question 2

Ramesh is currently 4 years older than Priya. If the sum of their ages is 36 years, then in how many years will Ramesh's age be twice Priya's current age?

Accepted Answer

Step 1: Let Priya's current age = x years. Then Ramesh's current age = (x + 4) years. Step 2: Sum of their ages is 36. So, x + (x + 4) = 36. This gives 2x + 4 = 36, therefore 2x = 32, so x = 16. Step 3: Priya's current age = 16 years, Ramesh's current age = 20 years. Step 4: We need to find after how many years (let's call it y) Ramesh's age will be twice Priya's current age. So, 20 + y = 2 × 16. Step 5: 20 + y = 32, therefore y = 12 years.

Question 3

The sum of the digits of a two-digit number is 13. If 27 is subtracted from the number, the digits get reversed. What is the original number?

Accepted Answer

Step 1: Let the tens digit be x and units digit be y. Then x + y = 13 and 10x + y − 27 = 10y + x. Step 2: From the second equation: 9x − 9y = 27 → x − y = 3. Step 3: Solve: x + y = 13 and x − y = 3 → 2x = 16 → x = 8, y = 5. Step 4: Original number = 85. Verify: 8 + 5 = 13 ✓; 85 − 27 = 58 (reversed) ✓. Therefore, answer is 85.

Question 4

If 6x - 8 = 4x + 6, find x.

Accepted Answer

Step 1: Start with 6x - 8 = 4x + 6. Step 2: Subtract 4x from both sides: 2x - 8 = 6. Step 3: Add 8 to both sides: 2x = 14. Step 4: Divide both sides by 2: x = 7. Therefore, x = 7.

Question 5

If 5x + 12 = 37, find the value of x.

Accepted Answer

Step 1: Start with 5x + 12 = 37. Step 2: Subtract 12 from both sides: 5x = 37 - 12 = 25. Step 3: Divide both sides by 5: x = 25 ÷ 5 = 5. Therefore, x = 5.

Question 6

If 2x + 3 = x + 8, what is the value of x?

Accepted Answer

Step 1: Start with 2x + 3 = x + 8. Step 2: Subtract x from both sides: x + 3 = 8. Step 3: Subtract 3 from both sides: x = 8 - 3 = 5. Therefore, x = 5.

Question 7

Solve: 4x - 7 = 2x + 5

Accepted Answer

Step 1: Start with 4x - 7 = 2x + 5. Step 2: Subtract 2x from both sides: 2x - 7 = 5. Step 3: Add 7 to both sides: 2x = 12. Step 4: Divide both sides by 2: x = 6. Therefore, x = 6.

Question 8

If 3x + 7 = 22, find the value of x.

Accepted Answer

Step 1: Start with 3x + 7 = 22. Step 2: Subtract 7 from both sides: 3x = 22 - 7 = 15. Step 3: Divide both sides by 3: x = 15 ÷ 3 = 5. Therefore, the answer is 5.

Question 9

If 4(x - 3) = 20, what is the value of x?

Accepted Answer

Step 1: Start with 4(x - 3) = 20. Step 2: Divide both sides by 4: x - 3 = 5. Step 3: Add 3 to both sides: x = 5 + 3 = 8. Therefore, the answer is 8.

Question 10

Solve: 2x + 3 = x + 8

Accepted Answer

Step 1: Start with 2x + 3 = x + 8. Step 2: Subtract x from both sides: 2x - x + 3 = 8, which gives x + 3 = 8. Step 3: Subtract 3 from both sides: x = 8 - 3 = 5. Therefore, the answer is 5.

Question 11

Solve for y: 3(y - 4) = 15

Accepted Answer

Step 1: Expand the left side: 3y - 12 = 15. Step 2: Add 12 to both sides: 3y = 15 + 12 = 27. Step 3: Divide both sides by 3: y = 27 ÷ 3 = 9. Therefore, y = 9.

Question 12

Solve for y: 5y - 12 = 2y + 9

Accepted Answer

Step 1: Start with 5y - 12 = 2y + 9. Step 2: Subtract 2y from both sides: 5y - 2y - 12 = 9, which gives 3y - 12 = 9. Step 3: Add 12 to both sides: 3y = 21. Step 4: Divide by 3: y = 7. Therefore, the answer is 7.

Question 13

Solve for m: 3m + 5 = 2m + 12

Accepted Answer

Step 1: Start with 3m + 5 = 2m + 12. Step 2: Subtract 2m from both sides: m + 5 = 12. Step 3: Subtract 5 from both sides: m = 12 - 5 = 7. Therefore, m = 7.

Question 14

A number when increased by 25% becomes 250. What is the original number?

Accepted Answer

Step 1: Let the original number be x. Step 2: When increased by 25%, the new value is x + 0.25x = 1.25x. Step 3: Set up the equation: 1.25x = 250. Step 4: Solve for x: x = 250/1.25 = 200. Therefore, the original number is 200.

Question 15

If 3(x + 2) − 5 = 2x + 9, then the value of x is:

Accepted Answer

Step 1: Expand the left side: 3x + 6 − 5 = 2x + 9. Step 2: Simplify: 3x + 1 = 2x + 9. Step 3: Subtract 2x from both sides: x + 1 = 9. Step 4: Subtract 1 from both sides: x = 8.

Question 16

If 5(x - 3) = 2(x + 6), then x equals:

Accepted Answer

Step 1: Expand both sides of the equation. Left side: 5x - 15. Right side: 2x + 12. Step 2: Set them equal: 5x - 15 = 2x + 12. Step 3: Move x terms to the left and constants to the right: 5x - 2x = 12 + 15. Step 4: Simplify: 3x = 27. Step 5: Divide both sides by 3: x = 9. Therefore, the answer is 9.

Question 17

A man is 4 times as old as his son. If the sum of their ages is 60 years, what is the son's age?

Accepted Answer

Step 1: Let the son's age be x years. Then the man's age is 4x years. Step 2: Set up the equation: x + 4x = 60. Step 3: Simplify: 5x = 60. Step 4: Solve for x: x = 12. Therefore, the son's age is 12 years.

Question 18

If 3x + 7 = 2x + 12, then the value of x is:

Accepted Answer

Step 1: Rearrange the equation by moving all x terms to the left and constants to the right. 3x - 2x = 12 - 7. Step 2: Simplify both sides. x = 5. Therefore, the answer is 5.

Question 19

The sum of two consecutive integers is 47. What is the larger integer?

Accepted Answer

Step 1: Let the two consecutive integers be x and x+1. Step 2: Set up the equation: x + (x+1) = 47. Step 3: Simplify: 2x + 1 = 47. Step 4: Solve for x: 2x = 46, so x = 23. Step 5: The larger integer is x + 1 = 24. Therefore, the answer is 24.

Question 20

If 2(3x + 5) - 4(x - 2) = 18, then x is equal to:

Accepted Answer

Step 1: Expand the left side. 2(3x + 5) = 6x + 10 and 4(x - 2) = 4x - 8. Step 2: Substitute: 6x + 10 - (4x - 8) = 18. Step 3: Simplify: 6x + 10 - 4x + 8 = 18. Step 4: Combine like terms: 2x + 18 = 18. Step 5: Solve: 2x = 0, so x = 0. Therefore, the answer is 0.

Question 21

A number is such that when it is divided by 4, the quotient is 15 more than when it is divided by 6. Find the number.

Accepted Answer

Step 1: Let the number be x. When divided by 4, quotient = x/4. When divided by 6, quotient = x/6. Step 2: Set up equation: x/4 = x/6 + 15. Step 3: Multiply through by 12: 3x = 2x + 180. Step 4: Solve: x = 180.

Question 22

The sum of three consecutive even numbers is 84. Find the largest of the three numbers.

Accepted Answer

Step 1: Let the three consecutive even numbers be x, x + 2, and x + 4. Step 2: Set up equation: x + (x + 2) + (x + 4) = 84. Step 3: Simplify: 3x + 6 = 84. Step 4: Subtract 6: 3x = 78. Step 5: Divide by 3: x = 26. Step 6: The three numbers are 26, 28, 30. The largest is 30.

Question 23

A sum of ₹1200 is divided among A, B, and C such that A gets twice as much as B, and C gets ₹100 more than B. How much does A get?

Accepted Answer

Step 1: Let B's share = x. Then A's share = 2x, and C's share = x + 100. Step 2: Total = 2x + x + (x+100) = 1200. Step 3: 4x + 100 = 1200. Step 4: 4x = 1100. Step 5: x = 275. Step 6: A's share = 2x = 2(275) = 550. Verification: A = 550, B = 275, C = 375. Sum = 550 + 275 + 375 = 1200 ✓.

SSC CHSL Linear Equations

SSC CHSL Linear Equations — Past Exam Questions

Linear Equations— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Linear Equations — Practice Questions

60-Second Revision — Linear Equations